90.14.1 problem 10

Internal problem ID [25229]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 243
Problem number : 10
Date solved : Thursday, October 02, 2025 at 11:59:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&={\mathrm e}^{2 t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t)-4*y(t) = exp(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{t} c_2 +{\mathrm e}^{-4 t} c_1 +\frac {{\mathrm e}^{2 t}}{6} \]

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 29

ode=D[y[t],{t,2}]+3*D[y[t],{t,1}]-4*y[t]==Exp[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {e^{2 t}}{6}+c_1 e^{-4 t}+c_2 e^t \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*y(t) - exp(2*t) + 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 4 t} + C_{2} e^{t} + \frac {e^{2 t}}{6} \]