Answer to Question #129305 in Differential Equations for Manal Malik Ali

Question

Solve given differential equations by separation of variables

dy/dx=y^3/x^2

Answer 1

dy/dx =y³/x²

dy/y³=dx/x²

integrating

-2*y^-2=-x^-1+c₁, c₁ is an integration constant,

y^-2=(x^-1+c₁)/2

y^-2=x^-1/2 +c₂, c₂ is an integration constant, c₂=c₁/2.

y=(x^-1/2+c₂)^-1/2