Question

$\frac{dy}{dx}=\frac{y+x\tan \left(\frac{y}{x}\right)}{x}\Rightarrow \sin \frac{y}{x}=$

• A. $c{x}^2$
• B. $cx$
• C. $c{x}^3$
• D. $c{x}^4$

Answer 1

Answer: (B)

$cx$

$Puty=vx$

$\Rightarrow \frac{dy}{dx}=v+x\frac{dv}{dx}$

$\Rightarrow v+x\frac{dv}{dx}=v+\tan v$

$\Rightarrow \int \cot vdv=\int \frac{dx}{x}+c$

$\Rightarrow \log \sin v=\log xc$

$\Rightarrow \sin \left(\frac{y}{x}\right)=cx$