90.15.2 problem 2

Internal problem ID [25249]
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 251
Problem number : 2
Date solved : Thursday, October 02, 2025 at 11:59:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=16 \,{\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)-15*y(t) = 16*exp(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-5 t} c_2 +{\mathrm e}^{3 t} c_1 -\frac {4 \,{\mathrm e}^{t}}{3} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 29

ode=D[y[t],{t,2}]+2*D[y[t],{t,1}]-15*y[t]==16*Exp[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {4 e^t}{3}+c_1 e^{-5 t}+c_2 e^{3 t} \end{align*}

✓ Sympy. Time used: 0.064 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-15*y(t) + 3*Derivative(y(t), (t, 2)) - 16*exp(-t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- \sqrt {5} t} + C_{2} e^{\sqrt {5} t} - \frac {4 e^{- t}}{3} \]