65.1.7 problem 5.4 (ii)

Internal problem ID [13710]
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 : Tuesday, January 28, 2025 at 05:55:46 AM
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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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