Internal problem ID [9227]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1648 (6.58).
ODE order: 2.
ODE degree: -1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-k \,x^{a} y^{b} \left (y^{\prime }\right )^{r}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x)-k*x^a*y(x)^b*diff(y(x),x)^r=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-(k*x^a*y[x]^b*y'[x]^r) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved