23.5.184 problem 184

Internal problem ID [6793]
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 : 184
Date solved : Tuesday, September 30, 2025 at 03:51:43 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

ode:=diff(y(x),x)+2*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);
 

\[ y = \left (c_5 x +c_3 \right ) \cos \left (x \right )+\left (c_4 x +c_2 \right ) \sin \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 35

ode=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 (-c_4 x+c_2-c_3) \cos (x)+(c_2 x+c_1+c_4) \sin (x)+c_5 \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 20

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

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