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: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t}={\mathrm e}^{-t}} \] With initial conditions \begin {align*} [x \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([diff(x(t)*exp(2*t),t)=exp(-t),x(0) = 3],x(t), singsol=all)
\[ x \left (t \right ) = -\left ({\mathrm e}^{-t}-4\right ) {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 18
DSolve[{D[x[t]*Exp[2*t],t]==Exp[-t],{x[0]==3}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-3 t} \left (4 e^t-1\right ) \]