65.3.1 problem 8.1 (i)

Internal problem ID [13719]
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 (i)
Date solved : Tuesday, January 28, 2025 at 05:59:37 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=t^{3} \left (-x+1\right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

dsolve([diff(x(t),t)=t^3*(1-x(t)),x(0) = 3],x(t), singsol=all)
 

\[ x \left (t \right ) = 1+2 \,{\mathrm e}^{-\frac {t^{4}}{4}} \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 18

DSolve[{D[x[t],t]==t^3*(1-x[t]),{x[0]==3}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 2 e^{-\frac {t^4}{4}}+1 \]