MHT CET 2021 21th September Evening Shift | Differential Equations Question 64 | Mathematics

The general solution of the differential equation. $$\left(\frac{y}{x}\right) \cos \left(\frac{y}{x}\right) d x-\left[\left(\frac{x}{y}\right) \sin \left(\frac{y}{x}\right)+\cos \left(\frac{y}{x}\right)\right] d y=0$$ is

$$y^2 \sin \left(\frac{y}{x}\right)=k$$

$$\mathrm{x} \sin \left(\frac{\mathrm{y}}{\mathrm{x}}\right)=\mathrm{k}$$

$$\sin \left(\frac{y}{x}\right)=k$$

$$y \sin \left(\frac{y}{x}\right)=k$$

MHT CET 2021 21th September Evening Shift

MCQ (Single Correct Answer)

-0

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

8 gms

16 gms

2 gms

32 gms

MHT CET 2021 21th September Evening Shift

MCQ (Single Correct Answer)

-0

If $$m$$ is order and $$n$$ is degree of the differential equation $$\left(\frac{d^2 y}{d x^2}\right)^5+4 \frac{\left(\frac{d^2 y}{d x^2}\right)}{\left(\frac{d^3 y}{d x^3}\right)}+\left(\frac{d^3 y}{d x^3}\right)=x^2$$ then

$$\mathrm{m}=3, \mathrm{n}=1$$

$$\mathrm{m}=3, \mathrm{n}=2$$

$$\mathrm{m}=3, \mathrm{n}=3$$

$$\mathrm{m}=3, \mathrm{n}=5$$

MHT CET 2021 21th September Morning Shift

MCQ (Single Correct Answer)

-0

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

$$x^2\left(2 x y-y^2\right)=c$$

$$x^2\left(y^2-2 x y\right)=c$$

$$x\left(2 x y+y^2\right)=c$$

$$x^2\left(2 x y+y^2\right)=c$$

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