67.4.9 problem Problem 2(i)

Internal problem ID [14053]
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(i)
Date solved : Tuesday, January 28, 2025 at 06:13:16 AM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.376 (sec). Leaf size: 13

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

\[ y = \frac {{\mathrm e}^{-\frac {t}{2}} \left (t -2\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 19

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

\[ y(t)\to \frac {1}{2} e^{-t/2} (t-2) \]