60.7.241 problem 1832 (book 6.241)

Internal problem ID [11830]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1832 (book 6.241)
Date solved : Monday, January 27, 2025 at 11:43:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} F_{1,1}\left (x \right ) {y^{\prime }}^{2}+\left (\left (F_{2,1}\left (x \right )+F_{1,2}\left (x \right )\right ) y^{\prime \prime }+y \left (F_{1,0}\left (x \right )+F_{0,1}\left (x \right )\right )\right ) y^{\prime }+F_{2,2}\left (x \right ) {y^{\prime \prime }}^{2}+y \left (F_{2,0}\left (x \right )+F_{0,2}\left (x \right )\right ) y^{\prime \prime }+F_{0,0}\left (x \right ) y^{2}&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[x*F[0, 0]*y[x]^2 + x*F[1, 1]*D[y[x],{x,2}] + (x*F[0, 2] + x*F[2, 0])*y[x]*D[y[x],{x,2}] + x*F[2, 2]*D[y[x],{x,2}]^2 + D[y[x],x]*((x*F[0, 1] + x*F[1, 0])*y[x] + (x*F[1, 2] + x*F[2, 1])*D[y[x],{x,2}]) == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved