Homogeneous Equations

Here is a homogeneous equation in which the total degree of both the numerator and the denominator of the right-hand side is 2. The two parts of the solution list give branches of the integral curves in the form y=f (x).

This plots both branches together, showing the complete integral curves for several values of C[1].

If an initial condition is specified, DSolve picks the branch that passes through the initial point. The DSolve::bvnul message indicates that one branch of the general solution (the lower branch in the previous graph) did not give a solution satisfying the given initial condition y[1]=3.