74.11.1 problem 13

Internal problem ID [16180]
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 : 13
Date solved : Monday, March 31, 2025 at 02:46:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y&=8 \,{\mathrm e}^{2 t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(y(t),t),t)+y(t) = 8*exp(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \sin \left (t \right ) c_2 +\cos \left (t \right ) c_1 +\frac {8 \,{\mathrm e}^{2 t}}{5} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 25

ode=D[y[t],{t,2}]+y[t]==8*Exp[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {8 e^{2 t}}{5}+c_1 \cos (t)+c_2 \sin (t) \]

✓ Sympy. Time used: 0.063 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - 8*exp(2*t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} \sin {\left (t \right )} + C_{2} \cos {\left (t \right )} + \frac {8 e^{2 t}}{5} \]