Question

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

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

Answer 1

Answer: (A), (C)

The correct options are
A $y\sin y=x^2\ln x+c$
C $y\sin y=x^2\ln x-c$

$\frac{dy}{dx}=\frac{x(2\log x+1)}{\sin y+y\cos y}\Rightarrow \frac{dy}{dx}(\sin y+y\cos y)=x+2x\log x$
Integrating both sides
$\int \frac{dy}{dx}(\sin y+y\cos y)dx=\int (x+2x\log x)dx\Rightarrow y\sin y=x^2\log x+c$