7.19.8 problem 34

Internal problem ID [548]
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 : 34
Date solved : Wednesday, February 05, 2025 at 03:45:43 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime \prime }+13 x^{\prime \prime }+36 x&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=2\\ x^{\prime \prime }\left (0\right )&=0\\ x^{\prime \prime \prime }\left (0\right )&=-13 \end{align*}

✓ Solution by Maple

Time used: 0.204 (sec). Leaf size: 17

dsolve([diff(x(t),t$4)+13*diff(x(t),t$2)+36*x(t)=0,x(0) = 0, D(x)(0) = 2, (D@@2)(x)(0) = 0, (D@@3)(x)(0) = -13],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\sin \left (3 t \right )}{3}+\frac {\sin \left (2 t \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 22

DSolve[{D[x[t],{t,4}]+13*D[x[t],{t,2}]+36*x[t]==0,{x[0]==0,Derivative[1][x][0] ==2,Derivative[2][x][0] ==0,Derivative[3][x][0] ==-13}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{6} (3 \sin (2 t)+2 \sin (3 t)) \]