11.3.4 problem 11

Internal problem ID [1486]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 6.2, The Laplace Transform. Solution of Initial Value Problems. page 255
Problem number : 11
Date solved : Monday, January 27, 2025 at 04:57:52 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+4 y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.277 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 37

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

\[ y(t)\to -\frac {2}{3} e^t \left (\sqrt {3} \sin \left (\sqrt {3} t\right )-3 \cos \left (\sqrt {3} t\right )\right ) \]