Internal problem ID [9204]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1625 (6.35).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (y-\frac {3 f^{\prime }\relax (x )}{2 f \relax (x )}\right ) y^{\prime }-y^{3}-\frac {f^{\prime }\relax (x ) y^{2}}{2 f \relax (x )}+\frac {\left (f \relax (x )+\frac {f^{\prime }\relax (x )^{2}}{f \relax (x )^{2}}-f^{\prime \prime }\relax (x )\right ) y}{2 f \relax (x )}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x)+(y(x)-3/2*diff(f(x),x)/f(x))*diff(y(x),x)-y(x)^3-1/2*diff(f(x),x)/f(x)*y(x)^2+1/2*(f(x)+diff(f(x),x)^2/f(x)^2-diff(diff(f(x),x),x))/f(x)*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-y[x]^3 - (y[x]^2*Derivative[1][f][x])/(2*f[x]) + (y[x] - (3*Derivative[1][f][x])/(2*f[x]))*y'[x] + y[x]*(f[x] + Derivative[1][f][x]^2/f[x]^2 - Derivative[2][f][x]/(2*f[x])) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved