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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.

If the differential equation $\begin{vmatrix} f(x) & f'(x) \\ f'(x) & f''(x) \end{vmatrix} = 0$ holds for all $x$, with initial conditions $f(0) = 1$ and $f'(0) = 2$, then which of the following is true?

(A)

$f'(x) = -f(x)$

(B)

$f'(x) = f(x)$

(C)

$f'(x) = 2f(x)$

(D)

$f'(x) = 0$

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