68.12.3 problem 3

Internal problem ID [17597]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 3
Date solved : Thursday, October 02, 2025 at 02:26:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&={\mathrm e}^{3 t} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 25

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

\[ y = \frac {{\mathrm e}^{2 t} \left (2 c_1 \,{\mathrm e}^{3 t}-{\mathrm e}^{t}+2 c_2 \right )}{2} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 31

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

\begin{align*} y(t)&\to -\frac {e^{3 t}}{2}+c_1 e^{2 t}+c_2 e^{5 t} \end{align*}

✓ Sympy. Time used: 0.121 (sec). Leaf size: 20

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

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