63.4.18 problem 8

Internal problem ID [13061]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 04:50:49 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} x \left (0\right )&=\ln \left (2\right ) \end{align*}

✓ Solution by Maple

Time used: 0.100 (sec). Leaf size: 15

dsolve([diff(x(t),t)=t^2*exp(-x(t)),x(0) = ln(2)],x(t), singsol=all)
 

\[ x \left (t \right ) = -\ln \left (3\right )+\ln \left (t^{3}+6\right ) \]

✓ Solution by Mathematica

Time used: 0.278 (sec). Leaf size: 15

DSolve[{D[x[t],t]==t^2*Exp[-x[t]],{x[0]==Log[2]}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \log \left (\frac {1}{3} \left (t^3+6\right )\right ) \]