Internal problem ID [9340]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1762 (book 6.171).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Painleve, 3rd]]
Solve \begin {gather*} \boxed {x y y^{\prime \prime }-x \left (y^{\prime }\right )^{2}+y^{\prime } y+x \left (d +a y^{4}\right )+y \left (c +y^{2} b \right )=0} \end {gather*}
✗ Solution by Maple
dsolve(x*y(x)*diff(diff(y(x),x),x)-x*diff(y(x),x)^2+y(x)*diff(y(x),x)+x*(d+a*y(x)^4)+y(x)*(c+y(x)^2*b)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*(c + b*y[x]^2) + x*(d + a*y[x]^4) + y[x]*y'[x] - x*y'[x]^2 + x*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved