60.7.120 problem 1711 (book 6.120)

Internal problem ID [11709]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1711 (book 6.120)
Date solved : Monday, January 27, 2025 at 11:30:40 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime } y-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (y+1\right ) \left (b^{2} y^{2}-a^{2}\right )&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+(a*y(x)-1)*diff(y(x),x)-y(x)*(y(x)+1)*(b^2*y(x)^2-a^2)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved