Question

Solve:

$\frac{dy}{dx}=\frac{x(2\ln x+1)}{\sin y+y\cos y}$

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

Answer 1

The correct option is D $y\sin y=x^2\ln x+c$

Given $\frac{dy}{dx}=\frac{x(2\ln x+1)}{\sin y+\cos y}$

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

$\frac{dy}{dx}\times \sin y+y\times \frac{d\left(\sin y\right)}{dx}=\frac{{d(x}^2)}{dx}\times \ln x+x^2\times \frac{d\left(\ln x\right)}{dx}$

On integration

$y\sin y=x^2\ln x+c$