Solved Consider The Differential Equation 3xy Y 2 Dx X 2 Xy Dy Course Hero
Answer (1 of 3) This is not a homogeneous equation Set z=xy, so y=xz and dy=dxdz and the equation becomes z\,dx(z2)\,dx(z2)\,dz=0 hence (2z2)\,dx(z2)\,dz y = (xlnx)/(1lnx) We have dy/dx = (x^2y^2xy)/x^2 with y(1)=0 Which is a First Order Nonlinear Ordinary Differential Equation Let us attempt a substitution of the form y = vx Differentiating wrt x and applying the product rule, we get dy/dx = v x(dv)/dx Substituting into the initial ODE we get v x(dv)/dx = (x^2(vx)^2x(vx))/x^2 Then assuming that x ne 0 this
