74.11.14 problem 26

Internal problem ID [16193]
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 : 26
Date solved : Monday, March 31, 2025 at 02:46:28 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 5 y^{\prime \prime }+y^{\prime }-4 y&=-3 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=5*diff(diff(y(t),t),t)+diff(y(t),t)-4*y(t) = -3; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 27

ode=5*D[y[t],{t,2}]+D[y[t],t]-4*y[t]==-3; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to c_1 e^{4 t/5}+c_2 e^{-t}+\frac {3}{4} \]

✓ Sympy. Time used: 0.142 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*y(t) + Derivative(y(t), t) + 5*Derivative(y(t), (t, 2)) + 3,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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