Internal problem ID [10973]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 2(m).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-y-{\mathrm e}^{2 t}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 8
dsolve([diff(y(t),t)-y(t)=exp(2*t),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 10
DSolve[{y'[t]-y[t]==Exp[2*t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{2 t} \\ \end{align*}