90.18.8 problem 12

Internal problem ID [25280]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 4. Linear Constant Coefficient Differential Equations. Exercises at page 299
Problem number : 12
Date solved : Thursday, October 02, 2025 at 11:59:33 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{2 t} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 32

ode:=diff(diff(diff(diff(y(t),t),t),t),t)-5*diff(diff(y(t),t),t)+4*y(t) = exp(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left (t +12 c_4 \right ) {\mathrm e}^{2 t}}{12}+c_1 \,{\mathrm e}^{t}+c_2 \,{\mathrm e}^{-2 t}+c_3 \,{\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 45

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

\begin{align*} y(t)&\to e^{-2 t} \left (c_2 e^t+c_3 e^{3 t}+e^{4 t} \left (\frac {t}{12}-\frac {19}{144}+c_4\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 29

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

\[ y{\left (t \right )} = C_{2} e^{- 2 t} + C_{3} e^{- t} + C_{4} e^{t} + \left (C_{1} + \frac {t}{12}\right ) e^{2 t} \]