67.4.37 problem Problem 13(a)

Internal problem ID [14081]
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)
Date solved : Tuesday, January 28, 2025 at 06:13:47 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y&=8 \end{align*}

Using Laplace method 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: 8.210 (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)
 

\[ y = \cos \left (2 t \right )-\sin \left (2 t \right )+{\mathrm e}^{-t}+2 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 22

DSolve[{D[ y[t],{t,3}]+D[y[t],{t,2}]+4*D[y[t],t]+4*y[t]==8,{y[0]==4,Derivative[1][y][0] ==-3,Derivative[2][y][0] ==-3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t}-\sin (2 t)+\cos (2 t)+2 \]