Internal problem ID [9211]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1632.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime } y a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 29
dsolve(diff(diff(y(x),x),x)-2*a*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (c_{2} \sqrt {c_{1} a}+x \sqrt {c_{1} a}\right ) \sqrt {c_{1} a}}{a} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 34
DSolve[-2*a*y[x]*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {c_1} \tan \left (\sqrt {a} \sqrt {c_1} (x+c_2)\right )}{\sqrt {a}} \\ \end{align*}