Internal problem ID [9410]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1832 (book 6.241).
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {F_{1,1}\relax (x ) \left (y^{\prime }\right )^{2}+\left (\left (F_{2,1}\relax (x )+F_{1,2}\relax (x )\right ) y^{\prime \prime }+y \left (F_{1,0}\relax (x )+F_{0,1}\relax (x )\right )\right ) y^{\prime }+F_{2,2}\relax (x ) \left (y^{\prime \prime }\right )^{2}+y \left (F_{2,0}\relax (x )+F_{0,2}\relax (x )\right ) y^{\prime \prime }+F_{0,0}\relax (x ) y^{2}=0} \end {gather*}
✗ Solution by Maple
dsolve(F[1,1](x)*diff(y(x),x)^2+((F[2,1](x)+F[1,2](x))*diff(diff(y(x),x),x)+y(x)*(F[1,0](x)+F[0,1](x)))*diff(y(x),x)+F[2,2](x)*diff(diff(y(x),x),x)^2+y(x)*(F[2,0](x)+F[0,2](x))*diff(diff(y(x),x),x)+F[0,0](x)*y(x)^2=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x*F[0, 0]*y[x]^2 + x*F[1, 1]*y''[x] + (x*F[0, 2] + x*F[2, 0])*y[x]*y''[x] + x*F[2, 2]*y''[x]^2 + y'[x]*((x*F[0, 1] + x*F[1, 0])*y[x] + (x*F[1, 2] + x*F[2, 1])*y''[x]) == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved