The solution of the differential equation x^2 dy = - 2xydx is - Vidyadip

MCQ

The solution of the differential equation ${x^2}dy = - 2xydx$ is

A
$x{y^2} = c$
B
${x^2}{y^2} = c$
✓
${x^2}y = c$
D
$xy = c$

✓

Answer

Correct option: C.

${x^2}y = c$

c
(c) ${x^2}dy = - 2xydx$ ==> $\frac{1}{y}dy = - \frac{{2x}}{{{x^2}}}dx$

On integrating, $\log y = - 2\log x + \log c$

==> $\log y = \log {x^{ - 2}} + \log c$ ==> $\log y{x^2} = \log c$ or $y{x^2} = c$.

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