The solution of the differential equation $(x cos x - sin x + y x^{2}) d x + x^{3} d y = 0$ is equal to:

\frac{sin x}{x} + x y = c

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\frac{sin x}{x} + x = c

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\frac{sin x}{x} + y = c

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None of these

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Solution

The correct option is A $\frac{sin x}{x} + x y = c$
We have $(x cos x - sin x + y x^{2}) d x + x^{3} d y = 0$
$\Rightarrow \frac{x cos x - sin x}{x^{2}} d x + y d x + x d y = 0$
$\Rightarrow d (\frac{sin x}{x}) + d (x y) = d (c)$
$\Rightarrow \frac{sin x}{x} + x y = c$

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Similar questions

$y = \frac{s i n x}{x + c o s x}, t h e n \frac{d y}{d x} = ?$

y = x + sinx is the solution of which of these differential equations ?

\frac{d y}{d x} + \frac{y}{x}

$\int \frac{d x}{s i n x . s i n (x + α)}$ is equal to

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x

(1)

0 < x < \frac{π}{2}

(2)

\frac{π}{2} < x < π

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