Internal problem ID [10122]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1800 (book 6.209).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {y^{3} y^{\prime \prime }=a} \]
✓ Solution by Maple
Time used: 15.657 (sec). Leaf size: 46
dsolve(y(x)^3*diff(diff(y(x),x),x)-a=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (\left (c_{2} +x \right )^{2} c_{1}^{2}+a \right ) c_{1}}}{c_{1}} \\ y \left (x \right ) &= -\frac {\sqrt {\left (\left (c_{2} +x \right )^{2} c_{1}^{2}+a \right ) c_{1}}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.192 (sec). Leaf size: 63
DSolve[-a + y[x]^3*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {a+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}} \\ y(x)\to \frac {\sqrt {a+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}} \\ y(x)\to \text {Indeterminate} \\ \end{align*}