MHT CET
Mathematics
Differential Equations
Previous Years Questions

The solution of $$\frac{\mathrm{d} x}{\mathrm{~d} y}+\frac{x}{y}=x^2$$ is
The solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{y}{x}=\sin x$$ is
The solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1+y^2}{1+x^2}$$ is
A curve passes through the point $$\left(1, \frac{\pi}{6}\right)$$. Let the slope of the curve at each point $$(x, y)$$ be $$\frac{y}{x}+\sec \left(\f... The general solution of the differential equation$$\frac{\mathrm{d} y}{\mathrm{~d} x}+\left(\frac{3 x^2}{1+x^3}\right) y=\frac{1}{x^3+1}$$is The differential equation of all circles, passing through the origin and having their centres on the$$\mathrm{X}$$-axis, is The population$$\mathrm{P}=\mathrm{P}(\mathrm{t})$$at time$$\mathrm{t}$$of certain species follows the differential equation$$\frac{d P}{d t}=0.5...
The differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\sqrt{1-y^2}}{y}$$ determines a family of circles with
General solution of the differential equation $$\cos x(1+\cos y) \mathrm{d} x-\sin y(1+\sin x) \mathrm{d} y=0$$ is
General solution of the differential equation $$\log \left(\frac{d y}{d x}\right)=a x+b y$$ is
The differential equation of all circles which pass through the origin and whose centres lie on $$\mathrm{Y}$$-axis is
The differential equation of all parabolas, whose axes are parallel to $$\mathrm{Y}$$-axis, is
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
$$\text{I} : y^{\prime}=\frac{y+x}{x} ; \quad \text { II }: y^{\prime}=\frac{x^2+y}{x^3} ; \quad \text { III }: y^{\prime}=\frac{2 x y}{y^2-x^2}$$ S1 ...
The differential equation of the family of circles touching $$y$$-axis at the origin is
The general solution of the differential equation. $$\left(\frac{y}{x}\right) \cos \left(\frac{y}{x}\right) d x-\left[\left(\frac{x}{y}\right) \sin \l... If the half life period of a substance is 5 years, then the total amount of the substance left after 15 years, when initial amount is 64 gms is If$$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...
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
The differential equation of family of circles whose centres lie on $$\mathrm{X}$$-axis is
The general solution of the differential equation $$y(1+\log x)\left(\frac{d x}{d y}\right)-x \log x=0$$ is
The general solution of the differential equation $$\frac{d y}{d x}=\frac{x+2 y-1}{x+2 y+1}$$ is
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 $$p=\frac{d y}{d ... The general solution of the differential equation$$\cos x \cdot \sin y d x+\sin x \cdot \cos y d y=0$$is The differential equation of an ellipse whose major axis is twice its minor axis, is The general solution of$$\left(x \frac{d y}{d x}-y\right) \sin \frac{y}{x}=x^3 e^x$$is The population of a city increases at a rate proportional to the population at that time. If the population of the city increase from 20 lakhs to 40 l... A differential equation for the temperature 'T' of a hot body as a function of time, when it is placed in a bath which is held at a constant temperatu... The general solution of the differential equation$$\frac{d y}{d x}=\frac{x+y+1}{x+y-1}$$is given by The general solution of the differential equation$$x+y \frac{d y}{d x}=\sec \left(x^2+y^2\right)$$is The differential equation of all circles which pass through the origin and whose centre lie on Y-axis is An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts in 20 minutes,$$x_0 is the...
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