23.5.40 problem 40

Internal problem ID [6649]
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 : 40
Date solved : Tuesday, September 30, 2025 at 03:50:31 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 a^{2} y-a^{2} y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = c_1 \,{\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{-a x}+c_3 \,{\mathrm e}^{a x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to c_1 e^{-a x}+c_3 e^{a x}+c_2 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 22

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

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