63.15.4 problem 6(d)

Internal problem ID [13187]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 3, Laplace transform. Section 3.2.1 Initial value problems. Exercises page 156
Problem number : 6(d)
Date solved : Tuesday, January 28, 2025 at 05:12:07 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.179 (sec). Leaf size: 9

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

\[ x \left (t \right ) = {\mathrm e}^{t} \sin \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 11

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

\[ x(t)\to e^t \sin (t) \]