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  4. If sin x (dy/dx)+y cos x=x sinx, then (y-1) sin x=

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Q. If $sin\,x \frac{dy}{dx}+y\,cos\,x=x\,sinx$, then $\left(y-1\right)\,sin\,x=$

Differential Equations

Solution:

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