76.2.13 problem 13

Internal problem ID [17349]
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 : 13
Date solved : Tuesday, January 28, 2025 at 10:02:01 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 19

dsolve([diff(y(t),t)-y(t)=2*t*exp(2*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[{D[y[t],t]-y[t]==2*t*Exp[2*t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

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