54.7.35 problem 1630 (6.40)

Internal problem ID [12884]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1630 (6.40)
Date solved : Friday, October 03, 2025 at 03:50:22 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }-3 y y^{\prime }-3 a y^{2}-4 a^{2} y-b&=0 \end{align*}

✓ Maple. Time used: 0.087 (sec). Leaf size: 755

ode:=diff(diff(y(x),x),x)-3*y(x)*diff(y(x),x)-3*a*y(x)^2-4*a^2*y(x)-b = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 122.747 (sec). Leaf size: 1670

ode=-b - 4*a^2*y[x] - 3*a*y[x]^2 - 3*y[x]*D[y[x],x] + D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(-4*a**2*y(x) - 3*a*y(x)**2 - b - 3*y(x)*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-a*(4*a + 3*y(x))*y(x) - b + Derivative(y(x), (x, 2)))/(3*y(x)) + Derivative(y(x), x) cannot be solved by the factorable group method