Internal problem ID [5862]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y=3 \sin \left (t \right )-5 \cos \left (t \right )} \]
✓ Solution by Maple
Time used: 0.625 (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)
\[ y \left (t \right ) = \frac {\left (5 t^{2}+\left (8 c_{3} -6\right ) t +8 c_{1} -10\right ) \cos \left (t \right )}{8}-\frac {3 \sin \left (t \right ) \left (t^{2}+\left (-\frac {8 c_{4}}{3}+\frac {10}{3}\right ) t -\frac {8 c_{2}}{3}-2\right )}{8} \]
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 56
DSolve[y''''[t]+2*y''[t]+y[t]==3*Sin[t]-5*Cos[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{16} \left (\left (10 t^2+2 (-3+8 c_2) t-25+16 c_1\right ) \cos (t)+\left (-6 t^2+2 (-15+8 c_4) t+3+16 c_3\right ) \sin (t)\right ) \]