Internal problem ID [3792]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1085.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{4} \left (y^{\prime }\right )^{3}-6 y^{\prime } x +2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.453 (sec). Leaf size: 123
dsolve(y(x)^4*diff(y(x),x)^3-6*x*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {2}\, \sqrt {x} \\ y \relax (x ) = -\sqrt {2}\, \sqrt {x} \\ y \relax (x ) = 0 \\ y \relax (x ) = \frac {\left (-4 c_{1}^{3}+24 c_{1} x \right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {\left (-4 c_{1}^{3}+24 c_{1} x \right )^{\frac {1}{3}}}{4}-\frac {i \sqrt {3}\, \left (-4 c_{1}^{3}+24 c_{1} x \right )^{\frac {1}{3}}}{4} \\ y \relax (x ) = -\frac {\left (-4 c_{1}^{3}+24 c_{1} x \right )^{\frac {1}{3}}}{4}+\frac {i \sqrt {3}\, \left (-4 c_{1}^{3}+24 c_{1} x \right )^{\frac {1}{3}}}{4} \\ y \relax (x ) = c_{1} \sqrt {x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 69.986 (sec). Leaf size: 22649
DSolve[y[x]^4 (y'[x])^3 -6 x y'[x] +2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
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