23.4.12 problem 12

Internal problem ID [6314]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 02:45:46 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 89

ode:=diff(diff(y(x),x),x) = a0+a1*y(x)+a2*y(x)^2+a3*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} -6 \int _{}^{y}\frac {1}{\sqrt {18 \operatorname {a3} \,\textit {\_a}^{4}+24 \operatorname {a2} \,\textit {\_a}^{3}+36 \operatorname {a1} \,\textit {\_a}^{2}+72 \operatorname {a0} \textit {\_a} +36 c_1}}d \textit {\_a} -x -c_2 &= 0 \\ 6 \int _{}^{y}\frac {1}{\sqrt {18 \operatorname {a3} \,\textit {\_a}^{4}+24 \operatorname {a2} \,\textit {\_a}^{3}+36 \operatorname {a1} \,\textit {\_a}^{2}+72 \operatorname {a0} \textit {\_a} +36 c_1}}d \textit {\_a} -x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.753 (sec). Leaf size: 1016

ode=D[y[x],{x,2}] == a0 + a1*y[x] + a2*y[x]^2 + a3*y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
a0 = symbols("a0") 
a1 = symbols("a1") 
a2 = symbols("a2") 
a3 = symbols("a3") 
y = Function("y") 
ode = Eq(-a0 - a1*y(x) - a2*y(x)**2 - a3*y(x)**3 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out