1
MHT CET 2021 24th September Evening Shift
+2
-0

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

A
$$\tan ^{-1} e^x-\tan ^{-1} y=0$$
B
$$\tan ^{-1} e^x+\tan ^{-1} y=\frac{\pi}{2}$$
C
$$2 \tan ^{-1} e^x+\tan ^{-1} y=\frac{3 \pi}{4}$$
D
$$\tan ^{-1} e^x-\tan ^{-1} y=\frac{3 \pi}{4}$$
2
MHT CET 2021 24th September Evening Shift
+2
-0

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.

A
2 and 2
B
1 and 2
C
1 and 1
D
2 and 1
3
MHT CET 2021 24th September Evening Shift
+2
-0

A population P grew at the rate given by the equation $$\frac{dP}{dt}=0.5P$$, then the population will become double in

A
20 (log 2) years
B
10 (log 2) years
C
5 (log 2) years
D
12 (log 2) years
4
MHT CET 2021 24th September Evening Shift
+2
-0

The differential equation of all parabolas whose axis is $$y$$-axis, is

A
$$\frac{d^2 y}{d x^2}-\frac{d y}{d x}=0$$
B
$$x \frac{d^2 y}{d x^2}+\frac{d y}{d x}=0$$
C
$$x \frac{d^2 y}{d x^2}-\frac{d y}{d x}=0$$
D
$$\frac{d^2 y}{d x^2}-y=0$$
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