Internal problem ID [11654]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=x -\frac {1}{3} x^{3}} \] With initial conditions \begin {align*} [y \left (-1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(y(x),x)=x-1/3*x^3,y(-1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (x^{2}-3\right )^{2}}{12}+\frac {4}{3} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 21
DSolve[{y'[x]==x-1/3*x^3,{y[-1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} \left (-x^4+6 x^2+7\right ) \]