Question

The solution of $\frac{dy}{dx}+y\cot x=2cosx$ is:

• A. $ysinx+co{s}^{2}x=c$
• B. $ycosx+si{n}^{2}x=c$
• C. $ysi{n}^{2}x-co{s}^{2}x=c$
• D. $yco{s}^{2}x-sinx=c$

Answer 1

The correct option is A $ysinx+co{s}^{2}x=c$

$\frac{dy}{dx}+\frac{y\cos x}{\sin x}=2\cos x$

$\Rightarrow \sin x\frac{dy}{dx}+y\cos x=\sin 2x$

$\Rightarrow y\sin x=\frac{-\cos 2x}{2}+c$

$y\sin x=-{\cos }^2+c_1$ $[c{+}^1{/}_2=c_1]$

$\Rightarrow y\sin x+{\cos }^{2}x=c_1$