Question Number 114978 by srijachakraborty last updated on 22/Sep/20

    Solve    x^2 dy + y(x+y)dx=0

Answered by soumyasaha last updated on 22/Sep/20

Answered by Dwaipayan Shikari last updated on 22/Sep/20

x^2 (dy/dx)+y(x+y)=0  x^2 (dy/dx)+vx(x+vx)=0        y=vx       (dy/dx)=v+x(dv/dx)  (dy/dx)=−v(1+v)           x(dv/dx)=−2v−v^2   ∫(dv/(−2v−v^2 ))=∫(dx/x)  −∫(dv/(v(v+2)))=∫(dx/x)  −(1/2)∫(1/v)−(1/(v+2))dv=log(x)+C  (1/2)log(((v+2)/v))=log(Cx)  1+((2x)/y)=Cx^2   y=((2x)/(1−Cx^2 ))

Commented bysrijachakraborty last updated on 22/Sep/20

thank you sir