1
MHT CET 2021 20th September Evening Shift
+2
-0

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 $$p=\frac{d y}{d x}$$, then the value of $$m+n$$ is

A
2
B
3
C
4
D
5
2
MHT CET 2021 20th September Evening Shift
+2
-0

The general solution of the differential equation $$\cos x \cdot \sin y d x+\sin x \cdot \cos y d y=0$$ is

A
$$\sin x+\sin y=c$$
B
$$\sin x \cdot \sin y=c$$
C
$$\cos x+\cos y=c$$
D
$$\cos x \cdot \cos y=c$$
3
MHT CET 2021 20th September Evening Shift
+2
-0

The differential equation of an ellipse whose major axis is twice its minor axis, is

A
$$x+4 y \frac{d y}{d x}=0$$
B
$$x-4 y \frac{d y}{d x}=0$$
C
$$x+2 y \frac{d y}{d x}=0$$
D
None of these
4
MHT CET 2021 20th September Evening Shift
+2
-0

The general solution of $$\left(x \frac{d y}{d x}-y\right) \sin \frac{y}{x}=x^3 e^x$$ is

A
$$e^x(x-1)+\cos \frac{y}{x}+c=0$$
B
$$x e^x+\cos \frac{y}{x}+c=0$$
C
$$e^x(x+1)+\cos \frac{y}{x}+c=0$$
D
$$e x^x-\cos \frac{y}{x}+c=0$$
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