Internal problem ID [9286]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1707.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime } y-\left (y^{\prime }\right )^{2}+y^{\prime } y a +y^{2} b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.038 (sec). Leaf size: 43
dsolve(diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+a*y(x)*diff(y(x),x)+y(x)^2*b=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = {\mathrm e}^{\frac {{\mathrm e}^{-a x} c_{1}}{a}} {\mathrm e}^{-\frac {b x}{a}} {\mathrm e}^{-\frac {c_{2}}{a}} {\mathrm e}^{\frac {b}{a^{2}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 28
DSolve[b*y[x]^2 + a*y[x]*y'[x] - y'[x]^2 + y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 e^{-\frac {b x+c_1 e^{-a x}}{a}} \\ \end{align*}