Internal problem ID [9281]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1703 (book 6.112).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime \prime } y-\left (y^{\prime }\right )^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right )=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+exp(x)*y(x)*(c*y(x)^2+d)+exp(2*x)*(b+a*y(x)^4)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[E^x*y[x]*(d + c*y[x]^2) + E^(2*x)*(b + a*y[x]^4) - y'[x]^2 + y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved