60.7.58 problem 1648 (6.58)

Internal problem ID [11647]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1648 (6.58)
Date solved : Monday, January 27, 2025 at 11:29:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r}&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[-(k*x^a*y[x]^b*D[y[x],x]^r) + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved