88.12.3 problem 3

Internal problem ID [24059]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:56:30 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

\[ y = c_1 +c_2 x +c_3 \,{\mathrm e}^{-2 x}+c_4 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to \frac {1}{4} e^{-2 x} \left (c_1 e^{4 x}+c_2\right )+c_4 x+c_3 \end{align*}

✓ Sympy. Time used: 0.046 (sec). Leaf size: 20

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

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