90.25.5 problem 5

Internal problem ID [25386]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 379
Problem number : 5
Date solved : Friday, October 03, 2025 at 12:00:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y = \left (\frac {{\mathrm e}^{2 t}}{2}+{\mathrm e}^{t} c_1 +c_2 \right ) {\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 29

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

\begin{align*} y(t)&\to \frac {1}{2} e^t \left (e^{2 t}+2 c_2 e^t+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.122 (sec). Leaf size: 19

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

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