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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
MCQ
The solution of differential equation $dy - \sin x\sin ydx = 0$ is
  • ✓
    ${e^{\cos x}}\tan \frac{y}{2} = c$
  • B
    ${e^{\cos x}}\tan y = c$
  • C
    $\cos x\tan y = c$
  • D
    $\cos x\sin y = c$
✓

Answer

Correct option: A.
${e^{\cos x}}\tan \frac{y}{2} = c$
a
(a) $\int_{}^{} {\frac{{dy}}{{\sin y}}} = \int_{}^{} {\sin xdx} $ ==> $\log \tan \frac{y}{2} = - \cos x + c$

==> $\tan \frac{y}{2} = {e^{ - \cos x + c}}$ ==> ${e^{\cos x}}\tan \frac{y}{2} = {e^C} = c$.

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