Internal problem ID [11395]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }-t^{2} {\mathrm e}^{-x}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = \ln \left (2\right )] \end {align*}
✓ Solution by Maple
Time used: 0.11 (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: 0.474 (sec). Leaf size: 15
DSolve[{x'[t]==t^2*Exp[-x[t]],{x[0]==Log[2]}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \log \left (\frac {1}{3} \left (t^3+6\right )\right ) \]