Internal problem ID [11985]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 8, Separable equations. Exercises page 72
Problem number: 8.1 (iii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }-x t^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(diff(x(t),t)=t^2*x(t),x(t), singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{\frac {t^{3}}{3}} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 22
DSolve[x'[t]==t^2*x[t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{\frac {t^3}{3}} \\ x(t)\to 0 \\ \end{align*}