Internal problem ID [12345]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page
368
Problem number: Problem 13(a).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y=8} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = -3, y^{\prime \prime }\left (0\right ) = -3] \end {align*}
✓ Solution by Maple
Time used: 4.031 (sec). Leaf size: 20
dsolve([diff(y(t),t$3)+diff(y(t),t$2)+4*diff(y(t),t)+4*y(t)=8,y(0) = 4, D(y)(0) = -3, (D@@2)(y)(0) = -3],y(t), singsol=all)
\[ y \left (t \right ) = \cos \left (2 t \right )-\sin \left (2 t \right )+{\mathrm e}^{-t}+2 \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 22
DSolve[{y'''[t]+y''[t]+4*y'[t]+4*y[t]==8,{y[0]==4,y'[0]==-3,y''[0]==-3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t}-\sin (2 t)+\cos (2 t)+2 \]