Internal problem ID [3744]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 34
Problem number: 1027.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+2 y^{\prime } x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.187 (sec). Leaf size: 173
dsolve(diff(y(x),x)^3+2*x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\left (-6 \sqrt {x^{2}+3 c_{1}}-6 x \right )^{\frac {3}{2}}}{27}-\frac {2 \sqrt {-6 \sqrt {x^{2}+3 c_{1}}-6 x}\, x}{3} \\ y \relax (x ) = \frac {\left (-6 \sqrt {x^{2}+3 c_{1}}-6 x \right )^{\frac {3}{2}}}{27}+\frac {2 \sqrt {-6 \sqrt {x^{2}+3 c_{1}}-6 x}\, x}{3} \\ y \relax (x ) = -\frac {\left (6 \sqrt {x^{2}+3 c_{1}}-6 x \right )^{\frac {3}{2}}}{27}-\frac {2 \sqrt {6 \sqrt {x^{2}+3 c_{1}}-6 x}\, x}{3} \\ y \relax (x ) = \frac {\left (6 \sqrt {x^{2}+3 c_{1}}-6 x \right )^{\frac {3}{2}}}{27}+\frac {2 \sqrt {6 \sqrt {x^{2}+3 c_{1}}-6 x}\, x}{3} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^3 +2 x y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out