60.7.171 problem 1762 (book 6.171)

Internal problem ID [11760]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1762 (book 6.171)
Date solved : Monday, January 27, 2025 at 11:34:17 PM
CAS classification : [[_Painleve, `3rd`]]

\begin{align*} x y y^{\prime \prime }-x {y^{\prime }}^{2}+y^{\prime } y+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right )&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[y[x]*(c + b*y[x]^2) + x*(d + a*y[x]^4) + y[x]*D[y[x],x] - x*D[y[x],x]^2 + x*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved