# Differential Equations · Mathematics · MHT CET

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MHT CET 2023 14th May Evening Shift
If the slope of the tangent of the curve at any point is equal to $$-y+\mathrm{e}^{-x}$$, then the equation of the curve passing through origin is...
MHT CET 2023 14th May Evening Shift
If a body cools from $$80^{\circ} \mathrm{C}$$ to $$50^{\circ} \mathrm{C}$$ in the room temperature of $$25^{\circ} \mathrm{C}$$ in 30 minutes, then t...
MHT CET 2023 14th May Evening Shift
The differential equation representing the family of curves $$y^2=2 \mathrm{c}(x+\sqrt{\mathrm{c}})$$, where $$\mathrm{c}$$ is a positive parameter, i...
MHT CET 2023 14th May Morning Shift
General solution of the differential equation $$\cos x(1+\cos y) \mathrm{d} x-\sin y(1+\sin x) \mathrm{d} y=0$$ is
MHT CET 2023 14th May Morning Shift
The differential equation of $$y=\mathrm{e}^x(\mathrm{a} \cos x+\mathrm{b} \sin x)$$ is
MHT CET 2023 13th May Evening Shift
If $$x d y=y(d x+y d y), y(1)=1, y(x)>0$$, then $$y(-3)$$ is
MHT CET 2023 13th May Evening Shift
The solution of $$(1+x y) y d x+(1-x y) x d y=0$$ is
MHT CET 2023 13th May Evening Shift
A radioactive substance, with initial mass $$m_0$$, has a half-life of $$h$$ days. Then, its initial decay rate is given by
MHT CET 2023 13th May Morning Shift
The solution of the differential equation $$\mathrm{e}^{-x}(y+1) \mathrm{d} y+\left(\cos ^2 x-\sin 2 x\right) y \mathrm{~d} x=0$$ at $$x=0$$, $$y=1$$ ...
MHT CET 2023 13th May Morning Shift
Rate of increase of bacteria in a culture is proportional to the number of bacteria present at that instant and it is found that the number doubles in...
MHT CET 2023 13th May Morning Shift
The particular solution of differential equation $$\mathrm{e}^{\frac{d y}{d x}}=(x+1), y(0)=3$$ is
MHT CET 2023 13th May Morning Shift
A right circular cone has height $$9 \mathrm{~cm}$$ and radius of base $$5 \mathrm{~cm}$$. It is inverted and water is poured into it. If at any insta...
MHT CET 2023 12th May Evening Shift
The solution of $$\mathrm{e}^{y-x} \frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{y(\sin x+\cos x)}{(1+y \log y)}$$ is
MHT CET 2023 12th May Evening Shift
Water flows from the base of rectangular tank, of depth 16 meters. The rate of flow of the water is proportional to the square root of depth at any ti...
MHT CET 2023 12th May Evening Shift
If $$(2+\sin x) \frac{\mathrm{d} y}{\mathrm{~d} x}+(y+1) \cos x=0$$ and $$y(0)=1$$, then $$y\left(\frac{\pi}{2}\right)$$ is
MHT CET 2023 12th May Morning Shift
The decay rate of radio active material at any time $$t$$ is proportional to its mass at that time. The mass is 27 grams when $$t=0$$. After three hou...
MHT CET 2023 12th May Morning Shift
The differential equation $$\cos (x+y) \mathrm{d} y=\mathrm{d} x$$ has the general solution given by
MHT CET 2023 12th May Morning Shift
If $$\frac{\mathrm{d} y}{\mathrm{~d} x}=y+3$$ and $$y(0)=2$$, then $$y(\log 2)=$$
MHT CET 2023 11th May Evening Shift
The solution of $$\frac{\mathrm{d} x}{\mathrm{~d} y}+\frac{x}{y}=x^2$$ is
MHT CET 2023 11th May Evening Shift
The solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{y}{x}=\sin x$$ is
MHT CET 2023 11th May Morning Shift
The solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1+y^2}{1+x^2}$$ is
MHT CET 2023 11th May Morning Shift
A curve passes through the point $$\left(1, \frac{\pi}{6}\right)$$. Let the slope of the curve at each point $$(x, y)$$ be $$\frac{y}{x}+\sec \left(\f... MHT CET 2023 10th May Evening Shift The general solution of the differential equation$$\frac{\mathrm{d} y}{\mathrm{~d} x}+\left(\frac{3 x^2}{1+x^3}\right) y=\frac{1}{x^3+1}$$is MHT CET 2023 10th May Evening Shift The differential equation of all circles, passing through the origin and having their centres on the$$\mathrm{X}$$-axis, is MHT CET 2023 10th May Morning Shift The population$$\mathrm{P}=\mathrm{P}(\mathrm{t})$$at time$$\mathrm{t}$$of certain species follows the differential equation$$\frac{d P}{d t}=0.5...
MHT CET 2023 10th May Morning Shift
The differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\sqrt{1-y^2}}{y}$$ determines a family of circles with
MHT CET 2023 10th May Morning Shift
General solution of the differential equation $$\cos x(1+\cos y) \mathrm{d} x-\sin y(1+\sin x) \mathrm{d} y=0$$ is
MHT CET 2023 9th May Evening Shift
General solution of the differential equation $$\log \left(\frac{d y}{d x}\right)=a x+b y$$ is
MHT CET 2023 9th May Evening Shift
The differential equation of all circles which pass through the origin and whose centres lie on $$\mathrm{Y}$$-axis is
MHT CET 2023 9th May Morning Shift
The differential equation of all parabolas, whose axes are parallel to $$\mathrm{Y}$$-axis, is
MHT CET 2023 9th May Morning Shift
The particular solution of the differential equation $$\left(1+y^2\right) \mathrm{d} x-x y \mathrm{~d} y=0$$ at $$x=1, y=0$$, represents
MHT CET 2022 11th August Evening Shift
The general solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{3 x+y}{x-y}$$ is (where $$C$$ is a constant of integratio...
MHT CET 2022 11th August Evening Shift
The differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\sqrt{1-y^2}}{y}$$ determines a family of circles with
MHT CET 2021 24th September Evening Shift
The particular solution of the differential equation $$\left(1+e^{2 x}\right) d y+e^x\left(1+y^2\right) d x=0$$ at $$x=0$$ and y = 1 is
MHT CET 2021 24th September Evening Shift
The order and degree of the differential equation $$\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0$$ are respectively.
MHT CET 2021 24th September Evening Shift
A population P grew at the rate given by the equation $$\frac{dP}{dt}=0.5P$$, then the population will become double in
MHT CET 2021 24th September Evening Shift
The differential equation of all parabolas whose axis is $$y$$-axis, is
MHT CET 2021 24th September Evening Shift
The general solution of the differential equation $$\frac{d y}{d x}=\tan \left(\frac{y}{x}\right)+\frac{y}{x}$$ is
MHT CET 2021 24th September Morning Shift
The particular solution of the differential equation $$\frac{d y}{d x}=\frac{x+y+1}{x+y-1}$$ when $$\mathrm{x}=\frac{2}{3}$$ and $$y=\frac{1}{3} ... MHT CET 2021 24th September Morning Shift The order of the differential equation whose solution is$$y=a \cos x+b \sin x+c e^{-x}$$is MHT CET 2021 24th September Morning Shift The general solution of the differential equation$$(2 y-1) d x-(2 x+3) d y=0$$is MHT CET 2021 24th September Morning Shift The differential equation of the family of parabolas with focus at the origin and the$$X$$-axis a axis, is MHT CET 2021 23rd September Evening Shift Radium decomposes at the rate proportional to the amount present at any time. If$$\mathrm{P} \%$$of amount disappears in one year, then amount of ra... MHT CET 2021 23rd September Evening Shift The differential equation obtained by eliminating A and B from$$y=A \cos \omega t+B \sin \omega t$$MHT CET 2021 23rd September Evening Shift The particular solution of the differential equation$$y(1+\log x) \frac{d x}{d y}-x \log x=0$$when$$x=e, y=e^2$$is MHT CET 2021 23rd September Evening Shift The order and degree of the differential equation$$\frac{d^2 y}{d x^2}=\sqrt{\frac{d y}{d x}}$$are respectively MHT CET 2021 23rd September Evening Shift The general solution of the differential equation$$\cos (x+y) \frac{d y}{d x}=1$$is MHT CET 2021 23th September Morning Shift The general solution of the differential equation$$\frac{d y}{d x}+\frac{y^2+y+1}{x^2+x+1}=0$$is MHT CET 2021 23th September Morning Shift The general solution of the differential equation$$\frac{d x}{d t}=\frac{x \log x}{t}$$is MHT CET 2021 23th September Morning Shift The particular solution of differential equation$$(x+y) d y+(x-y) d x=0$$at$$x=y=1$$is MHT CET 2021 23th September Morning Shift The general solution of the differential equation$$\frac{d y}{d x}=2^{y-x}$$is MHT CET 2021 23th September Morning Shift If the surrounding air is kept at$$25^{\circ} \mathrm{C}$$and a body cools from$$80^{\circ} \mathrm{C}$$to$$50^{\circ} \mathrm{C}$$in 30 minutes... MHT CET 2021 22th September Evening Shift The degree of the differential equation whose solution is$$y^2=8 a(x+a)$$, is MHT CET 2021 22th September Evening Shift A spherical raindrop evaporates at a rate proportional to its surface area. If its radius originally is 3 mm. and 1 hour later has been reduced to 2 m... MHT CET 2021 22th September Evening Shift The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is MHT CET 2021 22th September Evening Shift The particular solution of the differential equation$$\frac{d y}{d x}=\frac{y+1}{x^2-x}$$, when$$x=2$$and$$y=1$$is MHT CET 2021 22th September Evening Shift The general solution of$$\frac{d y}{d x}=\frac{x+y}{x-y}$$is MHT CET 2021 22th September Morning Shift The particular solution of the diffrential equation$$y(1+\log x)=\left(\log x^x\right) \frac{d y}{d x}$$, when$$y(e)=e^2$$is MHT CET 2021 22th September Morning Shift The general solution of$$\sin ^{-1}\left(\frac{d y}{d x}\right)=x+y$$is MHT CET 2021 22th September Morning Shift Solution of the differential equation$$\mathrm{y'=\frac{(x^2+y^2)}{xy}}$$, where y(1) =$$-$$2 is given by MHT CET 2021 22th September Morning Shift The differential equation of all family of lines$$y=m x+\frac{4}{m}$$obtained by eliminating the arbitrary constant$$\mathrm{m}$$is MHT CET 2021 21th September Evening Shift$$\text{I} : y^{\prime}=\frac{y+x}{x} ; \quad \text { II }: y^{\prime}=\frac{x^2+y}{x^3} ; \quad \text { III }: y^{\prime}=\frac{2 x y}{y^2-x^2}$$S1 ... MHT CET 2021 21th September Evening Shift The differential equation of the family of circles touching$$y$$-axis at the origin is MHT CET 2021 21th September Evening Shift The general solution of the differential equation.$$\left(\frac{y}{x}\right) \cos \left(\frac{y}{x}\right) d x-\left[\left(\frac{x}{y}\right) \sin \l...
MHT CET 2021 21th September Evening Shift
If the half life period of a substance is 5 years, then the total amount of the substance left after 15 years, when initial amount is 64 gms is
MHT CET 2021 21th September Evening Shift
If $$m$$ is order and $$n$$ is degree of the differential equation $$\left(\frac{d^2 y}{d x^2}\right)^5+4 \frac{\left(\frac{d^2 y}{d x^2}\right)}{\lef... MHT CET 2021 21th September Morning Shift The general solution of the differential equation$$\left(3 x y+y^2\right) d x+\left(x^2+x y\right) d y=0$$is MHT CET 2021 21th September Morning Shift The differential equation of family of circles whose centres lie on$$\mathrm{X}$$-axis is MHT CET 2021 21th September Morning Shift The general solution of the differential equation$$y(1+\log x)\left(\frac{d x}{d y}\right)-x \log x=0$$is MHT CET 2021 21th September Morning Shift The general solution of the differential equation$$\frac{d y}{d x}=\frac{x+2 y-1}{x+2 y+1}$$is MHT CET 2021 20th September Evening Shift If$$\mathrm{m}$$is order and$$\mathrm{n}$$is degree of the differential equation$$y=\frac{d p}{d x}+\sqrt{a^2 p^2-b^2}$$, where$$p=\frac{d y}{d ...
MHT CET 2021 20th September Evening Shift
The general solution of the differential equation $$\cos x \cdot \sin y d x+\sin x \cdot \cos y d y=0$$ is
MHT CET 2021 20th September Evening Shift
The differential equation of an ellipse whose major axis is twice its minor axis, is
MHT CET 2021 20th September Evening Shift
The general solution of $$\left(x \frac{d y}{d x}-y\right) \sin \frac{y}{x}=x^3 e^x$$ is
MHT CET 2021 20th September Evening Shift
The population of a city increases at a rate proportional to the population at that time. If the population of the city increase from 20 lakhs to 40 l...
MHT CET 2021 20th September Morning Shift
A differential equation for the temperature 'T' of a hot body as a function of time, when it is placed in a bath which is held at a constant temperatu...
MHT CET 2021 20th September Morning Shift
The general solution of the differential equation $$\frac{d y}{d x}=\frac{x+y+1}{x+y-1}$$ is given by
MHT CET 2021 20th September Morning Shift
The general solution of the differential equation $$x+y \frac{d y}{d x}=\sec \left(x^2+y^2\right)$$ is
MHT CET 2021 20th September Morning Shift
The differential equation of all circles which pass through the origin and whose centre lie on Y-axis is
MHT CET 2021 20th September Morning Shift
An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts in 20 minutes, $$x_0$$ is the...
MHT CET 2020 16th October Morning Shift
The differential equation obtained from the function $$y=a(x-a)^2$$ is
MHT CET 2020 16th October Morning Shift
The differential equation of all lines perpendicular to the line $$5 x+2 y+7=0$$ is
MHT CET 2020 16th October Morning Shift
The bacteria increases at the rate proportional to the number of bacteria present. If the original number '$$N$$' doubles in $$4 \mathrm{~h}$$, then t...
MHT CET 2020 16th October Morning Shift
The rate of decay of certain substance is directly proportional to the amount present at that instant. Initially, there are $$27 \mathrm{~gm}$$ of cer...
MHT CET 2020 16th October Morning Shift
The integrating factor of the differential equation $$\left(1+x^2\right) d t=\left(\tan ^{-1} x-t\right) d x$$ is
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