90.12.2 problem 2

Internal problem ID [25204]
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 213
Problem number : 2
Date solved : Thursday, October 02, 2025 at 11:58:03 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ y = \frac {{\mathrm e}^{3 t} c_1}{3}-\frac {{\mathrm e}^{t}}{2}+c_2 \]

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 26

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

\begin{align*} y(t)&\to -\frac {e^t}{2}+\frac {1}{3} c_1 e^{3 t}+c_2 \end{align*}

✓ Sympy. Time used: 0.091 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = C_{1} + C_{2} e^{3 t} - \frac {e^{t}}{2} \]