Internal problem ID [9337]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1758.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {\left (a y+b \right ) y^{\prime \prime }+c \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.059 (sec). Leaf size: 97
dsolve((a*y(x)+b)*diff(diff(y(x),x),x)+c*diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {b}{a} \\ y \relax (x ) = -\frac {\left (-c_{1} a x -c_{1} x c +\left (\frac {1}{\left (a +c \right ) \left (x c_{1}+c_{2}\right )}\right )^{-\frac {c}{a +c}} b -c_{2} a -c_{2} c \right ) \left (\frac {1}{\left (a +c \right ) \left (x c_{1}+c_{2}\right )}\right )^{\frac {c}{\left (1+\frac {c}{a}\right ) a}}}{a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.261 (sec). Leaf size: 31
DSolve[c*y'[x]^2 + (b + a*y[x])*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-b+(c_1 (a+c) (x+c_2)){}^{\frac {a}{a+c}}}{a} \\ \end{align*}