23.5.128 problem 128

Internal problem ID [6737]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 128
Date solved : Tuesday, September 30, 2025 at 03:51:16 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} 4 \cos \left (x \right ) {\mathrm e}^{-x}+y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 28

ode:=4*cos(x)/exp(x)+diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{3}}{6}+\frac {c_2 \,x^{2}}{2}+\cos \left (x \right ) {\mathrm e}^{-x}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 30

ode=(4*Cos[x])/E^x + D[y[x],{x,4}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.066 (sec). Leaf size: 24

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

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