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