90.18.7 problem 11

Internal problem ID [25279]
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 : 11
Date solved : Thursday, October 02, 2025 at 11:59:32 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=t \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

\[ y = \frac {t^{2}}{8}+\frac {\sin \left (2 t \right ) c_1}{2}-\frac {\cos \left (2 t \right ) c_2}{2}+c_3 \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 33

ode=D[y[t],{t,3}]+4*D[y[t],{t,1}]==t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{8} \left (t^2-4 c_2 \cos (2 t)+4 c_1 \sin (2 t)+8 c_3\right ) \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 22

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

\[ y{\left (t \right )} = C_{1} + C_{2} \sin {\left (2 t \right )} + C_{3} \cos {\left (2 t \right )} + \frac {t^{2}}{8} \]