82.26.2 problem Ex. 2

Internal problem ID [18803]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 67
Problem number : Ex. 2
Date solved : Monday, March 31, 2025 at 06:15:21 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-m^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 38

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-m^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sin \left (\sqrt {m}\, x \right )+c_2 \cos \left (\sqrt {m}\, x \right )+c_3 \,{\mathrm e}^{\sqrt {m}\, x}+c_4 \,{\mathrm e}^{-\sqrt {m}\, x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 53

ode=D[y[x],{x,4}]-m^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 e^{-\sqrt {m} x}+c_4 e^{\sqrt {m} x}+c_1 \cos \left (\sqrt {m} x\right )+c_3 \sin \left (\sqrt {m} x\right ) \]

✓ Sympy. Time used: 0.153 (sec). Leaf size: 53

from sympy import * 
x = symbols("x") 
m = symbols("m") 
y = Function("y") 
ode = Eq(-m**2*y(x) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x \sqrt [4]{m^{2}}} + C_{2} e^{x \sqrt [4]{m^{2}}} + C_{3} e^{- i x \sqrt [4]{m^{2}}} + C_{4} e^{i x \sqrt [4]{m^{2}}} \]