Internal problem ID [7842]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 262.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (2 y x^{2}-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.567 (sec). Leaf size: 75
dsolve((2*x^2*y(x)-x^3)*diff(y(x),x)+y(x)^3-4*x*y(x)^2+2*x^3=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (3 c_{1} x^{2}-\sqrt {3 c_{1} x^{2}+1}-1\right ) x}{c_{1} x^{2}-1}-x \\ y \relax (x ) = \frac {\left (3 c_{1} x^{2}+\sqrt {3 c_{1} x^{2}+1}-1\right ) x}{c_{1} x^{2}-1}-x \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.355 (sec). Leaf size: 132
DSolve[(2*x^2*y[x]-x^3)*y'[x]+y[x]^3-4*x*y[x]^2+2*x^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x^3-\sqrt {e^{2 c_1} x^2 \left (-3 x^2+e^{2 c_1}\right )}}{x^2+e^{2 c_1}} \\ y(x)\to \frac {2 x^3+\sqrt {e^{2 c_1} x^2 \left (-3 x^2+e^{2 c_1}\right )}}{x^2+e^{2 c_1}} \\ y(x)\to 2 x \\ y(x)\to -\sqrt {x^2} \\ y(x)\to \sqrt {x^2} \\ \end{align*}