12.18.25 problem section 9.2, problem 25

Internal problem ID [2139]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 25
Date solved : Tuesday, March 04, 2025 at 01:50:44 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=1\\ y^{\prime \prime \prime }\left (0\right )&=3 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 15

ode:=4*diff(diff(diff(diff(y(x),x),x),x),x)-13*diff(diff(y(x),x),x)+9*y(x) = 0; 
ic:=y(0) = 1, D(y)(0) = 3, (D@@2)(y)(0) = 1, (D@@3)(y)(0) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 2 \,{\mathrm e}^{x}-{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 18

ode=4*D[y[x],{x,4}]-13*D[y[x],{x,2}]+9*y[x]==0; 
ic={y[0]==1,Derivative[1][y][0] ==3,Derivative[2][y][0] ==1,Derivative[3][y][0]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 2 e^x-e^{-x} \]

✓ Sympy. Time used: 0.132 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 13*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 4)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 3, Subs(Derivative(y(x), (x, 2)), x, 0): 1, Subs(Derivative(y(x), (x, 3)), x, 0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 e^{x} - e^{- x} \]