Internal problem ID [14680]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number: 5.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }+9 y^{\prime \prime }=9 \,{\mathrm e}^{3 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(t),t$4)+9*diff(y(t),t$2)=9*exp(3*t),y(t), singsol=all)
\[ y \left (t \right ) = -\frac {c_{1} \cos \left (3 t \right )}{9}-\frac {c_{2} \sin \left (3 t \right )}{9}+\frac {{\mathrm e}^{3 t}}{18}+c_{3} t +c_{4} \]
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 41
DSolve[y''''[t]+9*y''[t]==9*Exp[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{3 t}}{18}+c_4 t-\frac {1}{9} c_1 \cos (3 t)-\frac {1}{9} c_2 \sin (3 t)+c_3 \]