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Solve: (3xy+y2) dx + (x2 + xy) dy = 0
Please give the steps after integration begins.
PS. ignore the previous ques....there was a mistake of square!
dy/dx=-(3xy+y2)/(x2+xy)
put y=vx
dy/dx=v+x(dv/dx)
v+x(dv/dx)=-(3vx2+v2x2)/(x2+vx2)
v+x(dv/dx)=-(3v+v2)/(1+v)
x(dv/dx)=-4v/(1+v)
∫((1+v)/v)dv=-∫(4/x)dx
ln(v)+v=-4lnx+c
(ln(v)+v+lnx4)=constant
ln(y/x)+lnx4+(y/x)=c.
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