75.16.21 problem 494

Internal problem ID [16923]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 494
Date solved : Monday, March 31, 2025 at 03:35:37 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-y&=1 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -1+c_1 \cos \left (x \right )+c_2 \,{\mathrm e}^{x}+c_3 \sin \left (x \right )+c_4 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 31

ode=D[y[x],{x,4}]-y[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^x+c_3 e^{-x}+c_2 \cos (x)+c_4 \sin (x)-1 \]

✓ Sympy. Time used: 0.080 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + Derivative(y(x), (x, 4)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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