87.17.43 problem 52

Internal problem ID [23635]
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 : 52
Date solved : Thursday, October 02, 2025 at 09:43:41 PM
CAS classification : [[_high_order, _quadrature]]

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

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

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

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 68

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

\begin{align*} u(x)&\to \int _1^x\int _1^{K[4]}\int _1^{K[3]}\int _1^{K[2]}\text {InverseFunction}[\text {NonCommutativeMultiply},2,2]\left [i,\frac {e^{-K[1]}}{e}\right ]dK[1]dK[2]dK[3]dK[4]+x (x (c_4 x+c_3)+c_2)+c_1 \end{align*}

✓ Sympy. Time used: 0.053 (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)) - exp(-x),0) 
ics = {} 
dsolve(ode,func=u(x),ics=ics)
 

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