23.5.130 problem 130

Internal problem ID [6739]
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 : 130
Date solved : Tuesday, September 30, 2025 at 03:51:17 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 31

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 38

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

\begin{align*} 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) \end{align*}

✓ Sympy. Time used: 0.090 (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)
 

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