60.7.10 problem 1600 (6.10)

Internal problem ID [11560]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1600 (6.10)
Date solved : Sunday, March 30, 2025 at 08:25:10 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 89

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

\begin{align*} -6 \int _{}^{y}\frac {1}{\sqrt {-18 a \,\textit {\_a}^{4}-24 b \,\textit {\_a}^{3}-36 c \,\textit {\_a}^{2}-72 d \textit {\_a} +36 c_1}}d \textit {\_a} -x -c_2 &= 0 \\ 6 \int _{}^{y}\frac {1}{\sqrt {-18 a \,\textit {\_a}^{4}-24 b \,\textit {\_a}^{3}-36 c \,\textit {\_a}^{2}-72 d \textit {\_a} +36 c_1}}d \textit {\_a} -x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 1.282 (sec). Leaf size: 1017

ode=d + c*y[x] + b*y[x]^2 + a*y[x]^3 + 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") 
c = symbols("c") 
d = symbols("d") 
y = Function("y") 
ode = Eq(a*y(x)**3 + b*y(x)**2 + c*y(x) + d + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out