60.7.24 problem 1614 (6.24)

Internal problem ID [11613]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1614 (6.24)
Date solved : Tuesday, January 28, 2025 at 06:07:02 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.137 (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)
 

\[ y = -c_{2} \operatorname {JacobiSN}\left (\frac {\left (-c_{1} a +\sqrt {-{\mathrm e}^{-2 a x}}\right ) c_{2}}{a}, i\right ) {\mathrm e}^{-a x} \]

✓ Solution by Mathematica

Time used: 2.330 (sec). Leaf size: 32

DSolve[2*a^2*y[x] - 2*y[x]^3 + 3*a*D[y[x],x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -i a c_1 e^{-a x} \text {sn}\left (\left .e^{-a x} c_1+c_2\right |-1\right ) \]