Question

Obtain the general solution of the differential equation


xdy - ydx + a( x^2+ y^2) dx=0​

Answer 1

Step-by-step explanation:

xdy−ydx=x2−y2dx

put y=vx and dy=vdx+xdv

x(vdx+xdv)−vxdx=x2−(vx)2dx

vxdx+x2dv−vxdx=x2(1−v2)dx

x2dv=x1−v2dx

xdv=1−v2dx

1−v2dv=xdx

integrate both side

sin−1v=lnx+C

put value of v

sin−1xy=lnx+C