60.7.172 problem 1763 (book 6.172)

Internal problem ID [11761]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1763 (book 6.172)
Date solved : Monday, January 27, 2025 at 11:34:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+b x y^{3}&=0 \end{align*}

✗ Solution by Maple

dsolve(x*y(x)*diff(diff(y(x),x),x)-x*diff(y(x),x)^2+a*y(x)*diff(y(x),x)+b*x*y(x)^3=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[b*x*y[x]^3 + a*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