23.5.188 problem 188

Internal problem ID [6797]
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 : 188
Date solved : Tuesday, September 30, 2025 at 03:51:46 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y+2 y^{\prime \prime \prime }+y^{\left (6\right )}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 48

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

\[ y = \left ({\mathrm e}^{\frac {3 x}{2}} \left (c_6 x +c_4 \right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )+{\mathrm e}^{\frac {3 x}{2}} \left (c_5 x +c_3 \right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_2 x +c_1 \right ) {\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 70

ode=y[x] + 2*D[y[x],{x,3}] + D[y[x],{x,6}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x} \left (c_6 x+e^{3 x/2} (c_2 x+c_1) \cos \left (\frac {\sqrt {3} x}{2}\right )+e^{3 x/2} (c_4 x+c_3) \sin \left (\frac {\sqrt {3} x}{2}\right )+c_5\right ) \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + 2*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 6)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{- x} + \left (\left (C_{3} + C_{4} x\right ) \sin {\left (\frac {\sqrt {3} x}{2} \right )} + \left (C_{5} + C_{6} x\right ) \cos {\left (\frac {\sqrt {3} x}{2} \right )}\right ) e^{\frac {x}{2}} \]