Internal problem ID [9194]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1615 (6.25).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (n +2\right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x)-(3*n+4)/n*diff(y(x),x)-2*(n+1)*(n+2)/n^2*y(x)*(y(x)^(n/(n+1))-1)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(-2*(1 + n)*(2 + n)*y[x]*(-1 + y[x]^(n/(1 + n))))/n^2 - ((4 + 3*n)*y'[x])/n + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved