Test Academy | For the exact differential equation, d u d x = − x u 2 2 + x 2 u which one of the following is the solution? u2 + 2x2 = constant, xu2 + u = constant, 1 2 x 2 u 2 + 2 u = constant, 1 2 u x 2 + 2 u = constant

Question

For the exact differential equation,

$\frac{d u}{d x} = \frac{- x u^{2}}{2 + x^{2} u}$

which one of the following is the solution?

Options :

u² + 2x² = constant
xu² + u = constant
$\frac{1}{2} x^{2} u^{2} + 2 u$ = constant
$\frac{1}{2} u x^{2} + 2 u$ = constant

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