67.4.2 problem Problem 2(b)

Internal problem ID [14046]
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 2(b)
Date solved : Tuesday, January 28, 2025 at 06:13:11 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 y^{\prime \prime }+16 y^{\prime }+17 y&=17 t -1 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 8.113 (sec). Leaf size: 17

dsolve([4*diff(y(t),t$2)+16*diff(y(t),t)+17*y(t)=17*t-1,y(0) = -1, D(y)(0) = 2],y(t), singsol=all)
 

\[ y = 2 \,{\mathrm e}^{-2 t} \sin \left (\frac {t}{2}\right )+t -1 \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 21

DSolve[{4*D[y[t],{t,2}]+16*D[y[t],t]+17*y[t]==17*t-1,{y[0]==-1,Derivative[1][y][0] ==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t+2 e^{-2 t} \sin \left (\frac {t}{2}\right )-1 \]