65.1.7 problem 5.4 (ii)

Internal problem ID [13631]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 5, Trivial differential equations. Exercises page 33
Problem number : 5.4 (ii)
Date solved : Wednesday, March 05, 2025 at 10:05:38 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=x -\frac {1}{3} x^{3} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=1 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 15

ode:=diff(y(x),x) = x-1/3*x^3; 
ic:=y(-1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {\left (x^{2}-3\right )^{2}}{12}+\frac {4}{3} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 21

ode=D[y[x],x]==x-1/3*x^3; 
ic={y[-1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{12} \left (-x^4+6 x^2+7\right ) \]

✓ Sympy. Time used: 0.129 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3/3 - x + Derivative(y(x), x),0) 
ics = {y(-1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {x^{4}}{12} + \frac {x^{2}}{2} + \frac {7}{12} \]