Question

Solution of $\frac{dy}{dx}=\frac{x\log x^2+x}{\sin y+y\cos y}$ is

• A. $y\sin y=x^2\log x+c$
• B. $y\sin y=x^2+c$
• C. $y\sin y=x^2+\log x+c$
• D. $y\sin y=x\log x+c$

Answer 1

The correct option is A $y\sin y=x^2\log x+c$

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

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

$(\sin y+y\cos y)dy=(x\log x^2+x)dx$

$d\left(y\sin y\right)=d\left(x^2\log x\right)$

On integrating, we get

$y\sin y=x^2\log x+C$