Internal problem ID [9289]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1711 (book 6.120).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime } y-\left (y^{\prime }\right )^{2}+\left (a y-1\right ) y^{\prime }-y \left (y+1\right ) \left (b^{2} y^{2}-a^{2}\right )=0} \end {gather*}
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[-(y[x]*(1 + y[x])*(-a^2 + b^2*y[x]^2)) + (-1 + a*y[x])*y'[x] - y'[x]^2 + y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved