Internal problem ID [8661]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1081.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {f \relax (x ) f^{\prime \prime \prime }\relax (x ) y^{\prime }}{f \relax (x )^{2}+b^{2}}-\frac {a^{2} f^{\prime }\relax (x )^{2} y}{f \relax (x )^{2}+b^{2}}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x)+f(x)*diff(diff(diff(f(x),x),x),x)/(f(x)^2+b^2)*diff(y(x),x)-a^2*diff(f(x),x)^2/(f(x)^2+b^2)*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-((a^2*y[x]*Derivative[1][f][x]^2)/(b^2 + f[x]^2)) + (f[x]*(f^3)[x]*y'[x])/(b^2 + f[x]^2) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved