10.1.13 problem 13

Internal problem ID [1110]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 13
Date solved : Monday, January 27, 2025 at 04:33:45 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 19

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

\[ y = \left (2 t -2\right ) {\mathrm e}^{2 t}+3 \,{\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 19

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

\[ y(t)\to e^t \left (2 e^t (t-1)+3\right ) \]