74.11.3 problem 15

Internal problem ID [16182]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 15
Date solved : Monday, March 31, 2025 at 02:46:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=2 \,{\mathrm e}^{3 t} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t)+3*y(t) = 2*exp(3*t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 25

ode=D[y[t],{t,2}]-4*D[y[t],t]+3*y[t]==2*Exp[3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to c_1 e^t+e^{3 t} \left (t-\frac {1}{2}+c_2\right ) \]

✓ Sympy. Time used: 0.204 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*y(t) - 2*exp(3*t) - 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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