Internal problem ID [3766]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1053.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
Solve \begin {gather*} \boxed {2 \left (y^{\prime }\right )^{3}+y^{\prime } x -2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 79
dsolve(2*diff(y(x),x)^3+x*diff(y(x),x)-2*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-\frac {c_{1}}{12}-\frac {\sqrt {c_{1}^{2}+24 x}}{12}\right )^{3}+\frac {\left (-\frac {c_{1}}{12}-\frac {\sqrt {c_{1}^{2}+24 x}}{12}\right ) x}{2} \\ y \relax (x ) = \left (-\frac {c_{1}}{12}+\frac {\sqrt {c_{1}^{2}+24 x}}{12}\right )^{3}+\frac {\left (-\frac {c_{1}}{12}+\frac {\sqrt {c_{1}^{2}+24 x}}{12}\right ) x}{2} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[2 (y'[x])^3 +x y'[x]-2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out