Internal problem ID [3321]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 579.
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 {x^{2} \left (x -2 y\right ) y^{\prime }-2 x^{3}+4 x y^{2}-y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 75
dsolve(x^2*(x-2*y(x))*diff(y(x),x) = 2*x^3-4*x*y(x)^2+y(x)^3,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: 1.24 (sec). Leaf size: 132
DSolve[x^2(x-2 y[x])y'[x]==2 x^3-4 x y[x]^2+y[x]^3,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*}