67.4.13 problem Problem 2(m)

Internal problem ID [14057]
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)
Date solved : Tuesday, January 28, 2025 at 06:13:19 AM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 7.676 (sec). Leaf size: 8

dsolve([diff(y(t),t)-y(t)=exp(2*t),y(0) = 1],y(t), singsol=all)
 

\[ y = {\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 10

DSolve[{D[y[t],t]-y[t]==Exp[2*t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{2 t} \]