75.16.44 problem 517

Internal problem ID [16938]
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 : 517
Date solved : Thursday, March 13, 2025 at 09:00:45 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=1 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 22

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(diff(y(x),x),x),x)+2*diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_4 x +c_{2} \right ) {\mathrm e}^{x}+\cos \left (x \right ) c_{1} +c_{3} \sin \left (x \right )+1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 30

ode=D[y[x],{x,4}]-2*D[y[x],{x,3}]+2*D[y[x],{x,2}]-2*D[y[x],x]+y[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.193 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 2*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)) - 2*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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