AP EAPCET 2025 - 27th May Morning Shift | Differential Equations Question 6 | Mathematics

If $A x^3+B x y=4$ ( $A$ and $B$ are arbitrary constants) is the general solution of the differential equation $F(x) \frac{d^2 y}{d x^2}+G(x) \frac{d y}{d x}-2 y=0$, then $F(l)+G(l)=$

AP EAPCET 2025 - 26th May Evening Shift

MCQ (Single Correct Answer)

-0

If $a$ and $b$ are arbitrary constants, then the differential equation corresponding to the family of curves $y=\tan (a x+b)$ is

$\left(1+x^2\right) y_2-2 y y_1+y=0$

$\left(1+y^2\right) y_2-2 y y_1^2=0$

$\left(1+x^2\right) y_2+2 y y_1^2=0$

$\left(1+y^2\right) y_2-2 y y_1^2+y=0$

AP EAPCET 2025 - 26th May Evening Shift

MCQ (Single Correct Answer)

-0

The general solution of the differential equation $x y(y+2) d y+\left(y^3-1\right) d x=0$ is

$\log |x+2 y|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{y-x}{\sqrt{3} x}\right)=C$

$\log |2 x-y|+\frac{2}{3} \tan ^{-1}\left(\frac{x-y}{\sqrt{3} x}\right)=C$

$\log |x y-x|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 y+1}{\sqrt{3}}\right)=C$

$\log |x+y|+\frac{2}{3} \tan ^{-1}\left(\frac{x-2 y}{\sqrt{3 x}}\right)=C$

AP EAPCET 2025 - 26th May Evening Shift

MCQ (Single Correct Answer)

-0

The general solution of the differential equation $\left(1+\sin ^2 x\right) \frac{d y}{d x}+y \sin 2 x=\cos x+\sin ^2 x \cos x$ is

$(\sin 2 x) y=\sin ^2 x+C$

$\left(1+\sin ^2 x\right) y=\sin x-\frac{\sin ^3 x}{3}+C$

$\left(1+\sin ^2 x\right) y=\sin x+\frac{\sin ^3 x}{3}+C$

$(\sin 2 x) y=\sin x+\sin ^2 x+C$

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