23.5.133 problem 133

Internal problem ID [6742]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 133
Date solved : Tuesday, September 30, 2025 at 03:51:18 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y+y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 38

ode:=y(x)+diff(diff(y(x),x),x)+diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {x}{2}} \left (\left (c_4 \,{\mathrm e}^{x}+c_2 \right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\sin \left (\frac {\sqrt {3}\, x}{2}\right ) \left (c_3 \,{\mathrm e}^{x}+c_1 \right )\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 56

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

\begin{align*} y(x)&\to e^{-x/2} \left (\left (c_2 e^x+c_4\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+\left (c_3 e^x+c_1\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 60

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

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