Internal problem ID [11663]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }-t^{3} \left (1-x\right )=0} \] 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: 0.074 (sec). Leaf size: 18
DSolve[{x'[t]==t^3*(1-x[t]),{x[0]==3}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to 2 e^{-\frac {t^4}{4}}+1 \]