88.16.5 problem 5

Internal problem ID [24110]
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 4. Linear equations. Exercises at page 116
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:59:19 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=x^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-diff(diff(y(x),x),x) = x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x^{3}-\frac {x^{5}}{20}+{\mathrm e}^{x} c_2 +{\mathrm e}^{-x} c_1 +c_3 x +c_4 \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 38

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

\begin{align*} y(x)&\to -\frac {x^5}{20}-x^3+c_4 x+c_1 e^x+c_2 e^{-x}+c_3 \end{align*}

✓ Sympy. Time used: 0.066 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{- x} + C_{4} e^{x} - \frac {x^{5}}{20} - x^{3} \]