7.19.5 problem 31

Internal problem ID [545]
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 : 31
Date solved : Monday, January 27, 2025 at 02:54:43 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }+x^{\prime \prime }-6 x^{\prime }&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.190 (sec). Leaf size: 24

dsolve([diff(x(t),t$3)+diff(x(t),t$2)-6*diff(x(t),t)=0,x(0) = 0, D(x)(0) = 1, (D@@2)(x)(0) = 1],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\left (6 \,{\mathrm e}^{5 t}-5 \,{\mathrm e}^{3 t}-1\right ) {\mathrm e}^{-3 t}}{15} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 25

DSolve[{D[x[t],{t,3}]+D[x[t],{t,2}]-6*D[x[t],t]==0,{x[0]==0,Derivative[1][x][0] ==1,Derivative[2][x][0] ==1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{15} \left (-e^{-3 t}+6 e^{2 t}-5\right ) \]