Question

xcos(y/x).dy/dx=ycos(y/x) + x ... find solution for this differential equation

Answer 1

\[x \cos \left( \frac{ y }{ x} \right)\frac{ dy }{dx}=y \cos \left( \frac{ y }{ x} \right)+x\]
\[Put y=vx,\frac{ dy }{dx }=v+x \frac{ dv }{ dx }\]
\[x \cos v \left( v+x \frac{ dv }{ dx } \right)=vx \cos v+x\]
\[vxcosv+x ^{2}\cos v \frac{ dv }{dx }=vx \cos v+x\]
\[x ^{2}\cos v \frac{ dv }{ dx }=x\]
\[x \cos v \frac{ dv }{ dx}=1\]
separate the variables and integrate

Answer 2

Thankyou :)