23.5.143 problem 143

Internal problem ID [6752]
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 : 143
Date solved : Tuesday, September 30, 2025 at 03:51:23 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 27 y-12 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 34

ode:=27*y(x)-12*diff(diff(y(x),x),x)+diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-3 x}+c_2 \,{\mathrm e}^{3 x}+c_3 \,{\mathrm e}^{\sqrt {3}\, x}+c_4 \,{\mathrm e}^{-\sqrt {3}\, x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 47

ode=27*y[x] - 12*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 c_1 e^{\sqrt {3} x}+c_2 e^{-\sqrt {3} x}+c_3 e^{-3 x}+c_4 e^{3 x} \end{align*}

✓ Sympy. Time used: 0.081 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(27*y(x) - 12*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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