65.3.3 problem 8.1 (iii)

Internal problem ID [13721]
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)
Date solved : Tuesday, January 28, 2025 at 05:59:43 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=t^{2} x \end{align*}

✓ Solution by Maple

Time used: 0.002 (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: 0.024 (sec). Leaf size: 22

DSolve[D[x[t],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*}