23.5.183 problem 183

Internal problem ID [6792]
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 : 183
Date solved : Tuesday, September 30, 2025 at 03:51:43 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 2 y^{\prime }-2 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\left (5\right )}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 28

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

\[ y = \left (c_3 x +c_2 \right ) {\mathrm e}^{x}+\left (c_4 \sin \left (x \right )+c_5 \cos \left (x \right )\right ) {\mathrm e}^{-x}+c_1 \]

✓ Mathematica. Time used: 0.125 (sec). Leaf size: 53

ode=2*D[y[x],x] - 2*D[y[x],{x,2}] - D[y[x],{x,3}] + D[y[x],{x,5}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} e^{-x} \left (2 e^{2 x} (c_4 (x-1)+c_3)-(c_1+c_2) \cos (x)+(c_2-c_1) \sin (x)\right )+c_5 \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*Derivative(y(x), x) - 2*Derivative(y(x), (x, 2)) - Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \left (C_{2} + C_{3} x\right ) e^{x} + \left (C_{4} \sin {\left (x \right )} + C_{5} \cos {\left (x \right )}\right ) e^{- x} \]