23.5.156 problem 156

Internal problem ID [6765]
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 : 156
Date solved : Tuesday, September 30, 2025 at 03:51:29 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y-4 y^{\prime }-3 y^{\prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=4*y(x)-4*diff(y(x),x)-3*diff(diff(y(x),x),x)+2*diff(diff(diff(y(x),x),x),x)+diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} \left (c_4 x +c_3 \right )+{\mathrm e}^{x} \left (c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to e^{-2 x} \left (c_3 e^{3 x}+x \left (c_4 e^{3 x}+c_2\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.129 (sec). Leaf size: 20

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

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