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 : Saturday, March 29, 2025 at 04:56:23 PM
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*}

✓ Maple. Time used: 0.151 (sec). Leaf size: 17

ode:=diff(diff(diff(diff(x(t),t),t),t),t)+13*diff(diff(x(t),t),t)+36*x(t) = 0; 
ic:=x(0) = 0, D(x)(0) = 2, (D@@2)(x)(0) = 0, (D@@3)(x)(0) = -13; 
dsolve([ode,ic],x(t),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.145 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(36*x(t) + 13*Derivative(x(t), (t, 2)) + Derivative(x(t), (t, 4)),0) 
ics = {x(0): 0, Subs(Derivative(x(t), t), t, 0): 2, Subs(Derivative(x(t), (t, 2)), t, 0): 0, Subs(Derivative(x(t), (t, 3)), t, 0): -13} 
dsolve(ode,func=x(t),ics=ics)
 

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