67.4.1 problem Problem 2(a)

Internal problem ID [14045]
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(a)
Date solved : Tuesday, January 28, 2025 at 06:13:11 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=9 t \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.332 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)+2*diff(y(t),t)+3*y(t)=9*t,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = 2 \,{\mathrm e}^{-t} \cos \left (\sqrt {2}\, t \right )+3 t -2 \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 13

DSolve[{D[y[t],{t,2}]+2*D[y[t],{t,2}]+3*y[t]==9*t,{y[0]==0,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 t-2 \sin (t) \]