Internal problem ID [10377]
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`]]
\[ \boxed {2 \,{\mathrm e}^{2 t} x+{\mathrm e}^{2 t} x^{\prime }-{\mathrm e}^{-t}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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: 0.062 (sec). Leaf size: 18
DSolve[{D[x[t]*Exp[2*t],t]==Exp[-t],{x[0]==3}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-3 t} \left (4 e^t-1\right ) \\ \end{align*}