10.1.14 problem 14

Internal problem ID [1111]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 14
Date solved : Monday, January 27, 2025 at 04:33:47 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 15

dsolve([2*y(t)+diff(y(t),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: 0.057 (sec). Leaf size: 19

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

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