Internal problem ID [7898]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 318.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {\left (3 x y^{3}-4 y x +y\right ) y^{\prime }+y^{2} \left (y^{2}-2\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve((3*x*y(x)^3-4*x*y(x)+y(x))*diff(y(x),x)+y(x)^2*(y(x)^2-2) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ x +\frac {1}{y \relax (x )^{2}}-\frac {c_{1}}{y \relax (x )^{2} \sqrt {y \relax (x )^{2}-2}} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.287 (sec). Leaf size: 2353
DSolve[y[x]^2*(-2 + y[x]^2) + (y[x] - 4*x*y[x] + 3*x*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
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