7.19.2 problem 28

Internal problem ID [542]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.3 (Translation and partial fractions). Problems at page 296
Problem number : 28
Date solved : Monday, January 27, 2025 at 02:54:42 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-6 x^{\prime }+8 x&=2 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.187 (sec). Leaf size: 18

dsolve([diff(x(t),t$2)-6*diff(x(t),t)+8*x(t)=2,x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {{\mathrm e}^{4 t}}{4}-\frac {{\mathrm e}^{2 t}}{2}+\frac {1}{4} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

DSolve[{D[x[t],{t,2}]-6*D[x[t],t]+8*x[t]==2,{x[0]==0,Derivative[1][x][0] ==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{4} \left (e^{2 t}-1\right )^2 \]