60.7.23 problem 1613 (6.23)

Internal problem ID [11573]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1613 (6.23)
Date solved : Sunday, March 30, 2025 at 08:28:43 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)+5*a*diff(y(x),x)-6*y(x)^2+6*a^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {WeierstrassP}\left (-\frac {{\mathrm e}^{-a x}}{a}+c_1 , 0, c_2\right ) {\mathrm e}^{-2 a x} \]

✓ Mathematica. Time used: 23.409 (sec). Leaf size: 35

ode=6*a^2*y[x] - 6*y[x]^2 + 5*a*D[y[x],x] + D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to a^2 c_1{}^2 e^{-2 a x} \wp \left (e^{-a x} c_1+c_2;0,-1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(6*a**2*y(x) + 5*a*Derivative(y(x), x) - 6*y(x)**2 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-6*a**2*y(x) + 6*y(x)**2 - Derivative(y(x), (x, 2)))/(5*a) cannot be solved by the factorable group method