48.3.6 problem Example 3.35

Internal problem ID [7530]
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 3.35
Date solved : Sunday, March 30, 2025 at 12:13:47 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=3 \sin \left (t \right )-5 \cos \left (t \right ) \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 45

ode:=diff(diff(diff(diff(y(t),t),t),t),t)+2*diff(diff(y(t),t),t)+y(t) = 3*sin(t)-5*cos(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left (5 t^{2}+\left (8 c_3 -6\right ) t +8 c_1 -10\right ) \cos \left (t \right )}{8}-\frac {3 \sin \left (t \right ) \left (t^{2}+\left (-\frac {8 c_4}{3}+\frac {10}{3}\right ) t -\frac {8 c_2}{3}-2\right )}{8} \]

✓ Mathematica. Time used: 0.119 (sec). Leaf size: 56

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

\[ y(t)\to \frac {1}{16} \left (\left (10 t^2+2 (-3+8 c_2) t-25+16 c_1\right ) \cos (t)+\left (-6 t^2+2 (-15+8 c_4) t+3+16 c_3\right ) \sin (t)\right ) \]

✓ Sympy. Time used: 0.271 (sec). Leaf size: 29

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

\[ y{\left (t \right )} = \left (C_{1} + t \left (C_{2} - \frac {3 t}{8}\right )\right ) \sin {\left (t \right )} + \left (C_{3} + t \left (C_{4} + \frac {5 t}{8}\right )\right ) \cos {\left (t \right )} \]