Internal problem ID [14698]
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: 23.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }=\cos \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(t),t$3)+3*diff(y(t),t$2)+2*diff(y(t),t)=cos(t),y(t), singsol=all)
\[ y \left (t \right ) = -c_{2} {\mathrm e}^{-t}+\frac {{\mathrm e}^{-2 t} c_{1}}{2}-\frac {3 \cos \left (t \right )}{10}+\frac {\sin \left (t \right )}{10}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.218 (sec). Leaf size: 36
DSolve[y'''[t]+3*y''[t]+2*y'[t]==Cos[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{10} \left (\sin (t)-3 \cos (t)-5 e^{-2 t} \left (2 c_2 e^t+c_1\right )\right )+c_3 \]