23.5.13 problem 13

Internal problem ID [6622]
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 : 13
Date solved : Tuesday, September 30, 2025 at 03:50:19 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y-2 y^{\prime }+y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=4*y(x)-2*diff(y(x),x)+diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 30

ode=4*y[x] - 2*D[y[x],x] + D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.113 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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