Internal problem ID [9192]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1613.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 27
dsolve(diff(diff(y(x),x),x)+5*a*diff(y(x),x)-6*y(x)^2+6*a^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \WeierstrassP \left (-\frac {{\mathrm e}^{-a x}}{a}+c_{1}, 0, c_{2}\right ) {\mathrm e}^{-2 a x} \]
✓ Solution by Mathematica
Time used: 0.858 (sec). Leaf size: 35
DSolve[6*a^2*y[x] - 6*y[x]^2 + 5*a*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a^2 c_1{}^2 e^{-2 a x} \wp \left (e^{-a x} c_1+c_2;0,-1\right ) \\ \end{align*}