Internal problem ID [8107]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 527.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}-x y^{4} y^{\prime }-y^{5}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 47
dsolve(diff(y(x),x)^3-x*y(x)^4*diff(y(x),x)-y(x)^5=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {3 \sqrt {3}}{2 x^{\frac {3}{2}}} \\ y \relax (x ) = \frac {3 \sqrt {3}}{2 x^{\frac {3}{2}}} \\ y \relax (x ) = 0 \\ y \relax (x ) = \sqrt {\frac {c_{1}^{10}}{\left (x c_{1}^{4}-1\right )^{2}}}\, c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 64
DSolve[-y[x]^5 - x*y[x]^4*y'[x] + y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{c_1 x-c_1{}^3} \\ y(x)\to 0 \\ y(x)\to \text {Indeterminate} \\ y(x)\to -\frac {3 \sqrt {3}}{2 x^{3/2}} \\ y(x)\to \frac {3 \sqrt {3}}{2 x^{3/2}} \\ \end{align*}