Internal problem ID [3786]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1077.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{2} \left (y^{\prime }\right )^{3}-y^{\prime } x +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.281 (sec). Leaf size: 189
dsolve(y(x)^2*diff(y(x),x)^3-x*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = -\frac {2 \sqrt {-24 c_{1}^{3}+27 c_{1} x -3 \sqrt {64 c_{1}^{6}-144 x c_{1}^{4}+108 x^{2} c_{1}^{2}-27 x^{3}}}}{9} \\ y \relax (x ) = \frac {2 \sqrt {-24 c_{1}^{3}+27 c_{1} x -3 \sqrt {64 c_{1}^{6}-144 x c_{1}^{4}+108 x^{2} c_{1}^{2}-27 x^{3}}}}{9} \\ y \relax (x ) = -\frac {2 \sqrt {-24 c_{1}^{3}+27 c_{1} x +3 \sqrt {64 c_{1}^{6}-144 x c_{1}^{4}+108 x^{2} c_{1}^{2}-27 x^{3}}}}{9} \\ y \relax (x ) = \frac {2 \sqrt {-24 c_{1}^{3}+27 c_{1} x +3 \sqrt {64 c_{1}^{6}-144 x c_{1}^{4}+108 x^{2} c_{1}^{2}-27 x^{3}}}}{9} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]^2 (y'[x])^3- x y'[x] + y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out