15.11.8 problem 8

Internal problem ID [3118]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 8
Date solved : Tuesday, March 04, 2025 at 04:00:29 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 28

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

\[ y = c_4 \,{\mathrm e}^{-x}+\frac {\left (4 c_2 +x \right ) {\mathrm e}^{x}}{4}+\cos \left (x \right ) c_{1} +c_3 \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 45

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

\[ y(x)\to \frac {e^x x}{4}-\frac {3 e^x}{8}+c_1 e^x+c_3 e^{-x}+c_2 \cos (x)+c_4 \sin (x) \]

✓ Sympy. Time used: 0.106 (sec). Leaf size: 26

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

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