Question

Suppose u(x) = cot x is an Integrating factor of the differential equation (sin x)? y" = 2y, find the general solution.

Answer 1

Ans:- According to the question

integrating factor is

$\Rightarrow$ $I.F.=e^{\int{p}dx}=Cotx$

$\Rightarrow$ $\int{pdx}=ln{Cotx}$

$\Rightarrow$ $p=-2\times Sec2x$

So then we arrange our question with respect to Integrating factor which has been given

As we see the question ? mark is coming $(sin x)? y" = 2y$ then instead of ? $2cosx$ written and $y''$ written as $y'$ .

Thus the question is $2{sin x}\times{cosx} y'= 2y$

$\Rightarrow y'-2y\times{Sec2x}=0$

Integrating factor is $Cotx$

then $y\times{Cotx}=\int{Cotx}\times{0}+c$

$\Rightarrow y\times{Cotx}=c$ where c is an arbitrary constant