76.2.14 problem 14

Internal problem ID [17350]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 10:02:03 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 15

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

\[ y = \frac {\left (t^{2}-1\right ) {\mathrm e}^{-2 t}}{2} \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 19

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

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