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 : Monday, January 27, 2025 at 03:04:41 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*}

✓ Solution by Maple

Time used: 0.081 (sec). Leaf size: 45

dsolve(diff(y(t),t$4)+2*diff(y(t),t$2)+y(t)=3*sin(t)-5*cos(t),y(t), singsol=all)
 

\[ y = \frac {\left (5 t^{2}+\left (8 c_3 -6\right ) t +8 c_{1} -10\right ) \cos \left (t \right )}{8}-\frac {3 \sin \left (t \right ) \left (t^{2}+\left (-\frac {8 c_4}{3}+\frac {10}{3}\right ) t -\frac {8 c_{2}}{3}-2\right )}{8} \]

✓ Solution by Mathematica

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

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

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