82.33.17 problem Ex. 17

Internal problem ID [18831]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 17
Date solved : Thursday, March 13, 2025 at 01:00:19 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 31

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

\[ y \left (x \right ) = c_4 \,{\mathrm e}^{-x}+\frac {\left (5 c_{1} -{\mathrm e}^{x}\right ) \cos \left (x \right )}{5}+c_{2} {\mathrm e}^{x}+c_3 \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 38

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

\[ y(x)\to c_1 e^x+c_3 e^{-x}+\left (-\frac {e^x}{5}+c_2\right ) \cos (x)+c_4 \sin (x) \]

✓ Sympy. Time used: 0.136 (sec). Leaf size: 27

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

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