MHT-CET

21. Differential Equations question bank (Mathematics)

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Q1.

The solution of $(1+xy)y \, dx + (1-xy)x \, dy = 0$ is:

(A)

$\log \left(\frac{x}{y}\right) + \frac{1}{xy} = k$,where $k$ is the constant of integration.

(B)

$\log \left(\frac{x}{y}\right) = \frac{1}{xy} + k$,where $k$ is the constant of integration.

(C)

$\log \left(\frac{x}{y}\right) + xy = k$,where $k$ is the constant of integration.

(D)

$\log \left(\frac{x}{y}\right) = xy + k$,where $k$ is the constant of integration.

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Q2.

The solution of the differential equation $e^{-x}(y+1) dy + (\cos^2 x - \sin 2x) y dx = 0$ at $x=0, y=1$ is

(A)

$(y+1) + e^x \cos^2 x = 2$

(B)

$y + \log y = e^x \cos^2 x$

(C)

$\log(y+1) + e^x \cos^2 x = 1$

(D)

$y + \log y + e^x \cos^2 x = 2$

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