Internal problem ID [815]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.1, Higher order linear differential equations. General theory. page 173
Problem number: 9.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 21
dsolve(diff(y(t),t$3)+2*diff(y(t),t$2)-diff(y(t),t)-2*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{t}+c_{3} {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 28
DSolve[y'''[t]+2*y''[t]-y'[t]-2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-2 t} \left (c_2 e^t+c_3 e^{3 t}+c_1\right ) \\ \end{align*}