MCQ
વિકલ સમીકરણ $\frac{{dy}}{{dx}} + y\cot x = 2\cos x$ નો ઉકેલ મેળવો.
- A$y\sin x + \cos 2x = 2c$
- B$2y\sin x + \cos x = c$
- C$y\sin x + \cos x = c$
- ✓$2y\sin x + \cos 2x = c$
It is linear equation of the form $\frac{{dy}}{{dx}} + Py = Q$
So, $I.F.$ $ = {e^{\int_{}^{} {Pdx} }} = {e^{\int_{}^{} {\cot xdx} }} = {e^{\log \sin x}} = \sin x$
Hence the solution is $y\sin x = \int_{}^{} {2\sin x\cos xdx + c} $
==> $y\sin x = - \frac{1}{2}\cos 2x + c$ ==> $2y\sin x + \cos 2x = c$.
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