Internal problem ID [9193]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1614.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.029 (sec). Leaf size: 33
dsolve(diff(diff(y(x),x),x)+3*a*diff(y(x),x)-2*y(x)^3+2*a^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{2} \mathrm {sn}\left (\left (-\frac {\sqrt {-{\mathrm e}^{-2 a x}}}{a}+c_{1}\right ) c_{2}| i\right ) {\mathrm e}^{-a x} \]
✓ Solution by Mathematica
Time used: 0.626 (sec). Leaf size: 32
DSolve[2*a^2*y[x] - 2*y[x]^3 + 3*a*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -i a c_1 e^{-a x} \text {sn}\left (\left .e^{-a x} c_1+c_2\right |-1\right ) \\ \end{align*}