76.2.17 problem 17

Internal problem ID [17353]
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 : 17
Date solved : Tuesday, January 28, 2025 at 10:02:09 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 14

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

\[ y(t)\to e^{2 t} (t+2) \]