Internal problem ID [9252]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1674 (book 6.83).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}+a \left ({\mathrm e}^{y}-1\right )=0} \end {gather*}
✗ Solution by Maple
dsolve(x^2*diff(diff(y(x),x),x)+a*(exp(y(x))-1)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[a*(-1 + E^y[x]) + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved