87.17.47 problem 56

Internal problem ID [23639]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 127
Problem number : 56
Date solved : Thursday, October 02, 2025 at 09:43:43 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} e i u^{\prime \prime \prime \prime }&=x^{4} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 32

ode:=e*i*diff(diff(diff(diff(u(x),x),x),x),x) = x^4; 
dsolve(ode,u(x), singsol=all);
 

\[ u = \frac {x^{8}}{1680 e i}+\frac {c_1 \,x^{3}}{6}+\frac {c_2 \,x^{2}}{2}+c_3 x +c_4 \]

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

ode=e*i*D[u[x],{x,4}]==x^4; 
ic={}; 
DSolve[{ode,ic},u[x],x,IncludeSingularSolutions->True]
 

\begin{align*} u(x)&\to \frac {x^8}{1680 e i}+x (x (c_4 x+c_3)+c_2)+c_1 \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
e = symbols("e") 
i = symbols("i") 
u = Function("u") 
ode = Eq(e*i*Derivative(u(x), (x, 4)) - x**4,0) 
ics = {} 
dsolve(ode,func=u(x),ics=ics)
 

\[ u{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + \frac {x^{8}}{1680 e i} \]