56.29.2 problem Ex 2

Internal problem ID [14234]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary. Page 117
Problem number : Ex 2
Date solved : Thursday, October 02, 2025 at 09:27:01 AM
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: 0.007 (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);
 

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

✓ Mathematica. Time used: 0.036 (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]
 

\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: 0.081 (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)
 

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