52.6.11 problem 31

Internal problem ID [8346]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. 7.3.1 TRANSLATION ON THE s-AXIS. Page 297
Problem number : 31
Date solved : Monday, January 27, 2025 at 03:49:18 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.531 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 18

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

\[ y(t)\to e^{-t} (e t+t+e-1) \]