90.14.2 problem 11

Internal problem ID [25230]
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 : 11
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 }-10 y&=7 \,{\mathrm e}^{2 t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(diff(y(t),t),t)-3*diff(y(t),t)-10*y(t) = 7*exp(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-2 t} c_2 +{\mathrm e}^{5 t} c_1 -\frac {7 \,{\mathrm e}^{2 t}}{12} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 31

ode=D[y[t],{t,2}]-3*D[y[t],{t,1}]-10*y[t]==7*Exp[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {7 e^{2 t}}{12}+c_1 e^{-2 t}+c_2 e^{5 t} \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-10*y(t) - 7*exp(2*t) - 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 2 t} + C_{2} e^{5 t} - \frac {7 e^{2 t}}{12} \]