Internal problem ID [14857]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 36.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y={\mathrm e}^{-t} \cos \left (2 t \right )+\sin \left (t \right ) {\mathrm e}^{-2 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 70
dsolve(diff(y(t),t$4)+6*diff(y(t),t$3)+18*diff(y(t),t$2)+30*diff(y(t),t)+25*y(t)=exp(-t)*cos(2*t)+exp(-2*t)*sin(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\left (-20 t +400 c_{3} -6\right ) \cos \left (t \right )^{2}-10 \left (t -40 c_{4} -\frac {21}{5}\right ) \sin \left (t \right ) \cos \left (t \right )+10 t -200 c_{3} +3\right ) {\mathrm e}^{-t}}{200}-\frac {{\mathrm e}^{-2 t} \left (\left (t -10 c_{1} +\frac {7}{10}\right ) \cos \left (t \right )-\frac {\left (t +20 c_{2} +\frac {1}{5}\right ) \sin \left (t \right )}{2}\right )}{10} \]
✓ Solution by Mathematica
Time used: 0.438 (sec). Leaf size: 77
DSolve[y''''[t]+6*y'''[t]+18*y''[t]+30*y'[t]+25*y[t]==Exp[-t]*Cos[2*t]+Exp[-2*t]*Sin[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{800} e^{-2 t} \left (-4 (20 t+9-200 c_2) \cos (t)-e^t (40 t-3-800 c_4) \cos (2 t)+8 (5 t+6+100 c_1) \sin (t)-2 e^t (10 t-27-400 c_3) \sin (2 t)\right ) \]