1
MHT CET 2021 23rd September Evening Shift
+2
-0

The differential equation obtained by eliminating A and B from $$y=A \cos \omega t+B \sin \omega t$$

A
$$\frac{d^2 y}{d t^2}+\omega^2 y=0$$
B
$$\frac{\mathrm{d}^2 y}{\mathrm{dt}^2}+\omega \mathrm{y}^2=0$$
C
$$\frac{d^2 y}{d t^2}-\omega^2 y=0$$
D
$$\frac{d^2 y}{d t^2}-\omega y^2=0$$
2
MHT CET 2021 23rd September Evening Shift
+2
-0

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

A
$$y^2=e^4 \log x$$
B
$$y=e^2 \log x$$
C
$$y=x^2 \log x$$
D
$$y=e x \log x$$
3
MHT CET 2021 23rd September Evening Shift
+2
-0

The order and degree of the differential equation $$\frac{d^2 y}{d x^2}=\sqrt{\frac{d y}{d x}}$$ are respectively

A
2, 3
B
3, 3
C
2, 2
D
1, 3
4
MHT CET 2021 23rd September Evening Shift
+2
-0

The general solution of the differential equation $$\cos (x+y) \frac{d y}{d x}=1$$ is

A
$$y=\tan (x+y)+c$$
B
$$y=\sec (x+y)+c$$
C
$$y=\tan \left(\frac{x+y}{2}\right)+c$$
D
$$y=\cot \left(\frac{x+y}{2}\right)+c$$
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