Solution of differential equation dy dx = 2xy is - Vidyadip

MCQ

Solution of differential equation $\frac{{dy}}{{dx}} = 2xy$ is

✓
$y = c{e^{{x^2}}}$
B
${y^2} = 2{x^2} + c$
C
$y = {e^{ - {x^2}}} + c$
D
$y = {x^2} + c$

✓

Answer

Correct option: A.

$y = c{e^{{x^2}}}$

a
(a) $\int_{}^{} {\frac{{dy}}{y} = \int_{}^{} {2xdx} } $ ==> ${\log _e}y = {x^2} + c$

==> $y = {e^{{x^2} + c}} = {e^c}{e^{{x^2}}}$ ==> $y = c{e^{{x^2}}}$.

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