72.21.7 problem 7

Internal problem ID [14977]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 6. Laplace transform. Section 6.6. page 624
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 07:26:07 AM
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 (0\right )&=1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 8.754 (sec). Leaf size: 14

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

\[ y = \left (3 t +1\right ) {\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 16

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

\[ y(t)\to e^{-t} (3 t+1) \]