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Question

Mathematics Question on Differential equations

If sin xdydx+y cos x=x sinxsin\,x \frac{dy}{dx}+y\,cos\,x=x\,sinx, then (y−1) sin x=\left(y-1\right)\,sin\,x=

A

c−x sinxc-x\,sinx

B

c+x cosxc+x\,cosx

C

c−x cosxc-x\,cosx

D

c+x sinxc+x\,sinx

Answer

c−x cosxc-x\,cosx

Explanation

Solution

dydx+(sin x⋅y)=x sin x \frac{dy}{dx}+\left(sin\,x\cdot y\right)=x\,sin\,x ⇒y sin x=∫x sin x dx=−x cos x+sin x+c\Rightarrow y\,sin\,x=\int x\,sin\,x\,dx=-x\,cos\,x+sin\,x+c ⇒(y−1) sin x=c−x cos x\Rightarrow \left(y-1\right)\,sin\,x=c-x\,cos\,x.