76.2.17 problem 17

Internal problem ID [17282]
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 : Monday, March 31, 2025 at 03:48:40 PM
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*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 12

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

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

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

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

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

✓ Sympy. Time used: 0.149 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) - exp(2*t) + Derivative(y(t), t),0) 
ics = {y(0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

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