48.3.5 problem Example 3.34

Internal problem ID [7529]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page 181
Problem number : Example 3.34
Date solved : Sunday, March 30, 2025 at 12:13:45 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

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

\[ y = {\mathrm e}^{t} \left (\frac {2}{3} t^{3}+c_1 +c_2 t +c_3 \,t^{2}\right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 34

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

\[ y(t)\to \frac {1}{3} e^t \left (2 t^3+3 c_3 t^2+3 c_2 t+3 c_1\right ) \]

✓ Sympy. Time used: 0.265 (sec). Leaf size: 19

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

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