11.6.4 problem 1.2-1 (d)

Internal problem ID [3441]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-1, page 12
Problem number : 1.2-1 (d)
Date solved : Tuesday, September 30, 2025 at 06:38:28 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(y(t),t) = 2*y(t)+exp(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (t +c_1 \right ) {\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 15

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

\begin{align*} y(t)&\to e^{2 t} (t+c_1) \end{align*}

✓ Sympy. Time used: 0.085 (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 = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} + t\right ) e^{2 t} \]