Now, dydx=x^2+2y or, #160; y dy=x^2 dx+2 dx Now integrating we have, y^22=x^33+2x+c [ Where c is integrating constant]. ...

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Particular Solution of a Differential Equation

Solve: dydx=...

Question

Solve:
$\frac{d y}{d x} = \frac{x^{2} + 2}{y}$ .

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Solution

Now,
$\frac{d y}{d x} = \frac{x^{2} + 2}{y}$
or, $y d y = x^{2} d x + 2 d x$
Now integrating we have,
$\frac{y^{2}}{2} = \frac{x^{3}}{3} + 2 x + c$ [ Where $c$ is integrating constant].

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