The solution of the differential equation dy dx = y (y^2-x) is - Vidyadip

MCQ

The solution of the differential equation $\frac{dy}{dx}= \frac{y}{(y^2-x)}$ is

A
$y^3 -xy = c$
✓
$y^3 -3xy = c$
C
$y^3 + 3xy = c$
D
$y^3 + xy = c$

✓

Answer

Correct option: B.

$y^3 -3xy = c$

b
$\frac{d x}{d y}=y-\frac{x}{y} \Rightarrow \frac{d x}{d y}+\frac{1}{y} \cdot x=y$

$\therefore $ solution is $x . y=\int y^{2} d y+c \Rightarrow x . y=\frac{y^{3}}{3}+c$

$\Rightarrow \mathrm{y}^{3}-3 \mathrm{xy}=\mathrm{c}$

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