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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
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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