69.16.22 problem 495

Internal problem ID [18282]
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 : 495
Date solved : Thursday, October 02, 2025 at 03:10:06 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 55

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

\[ y = -\frac {{\mathrm e}^{-\frac {x}{2}} \left (c_3 \sqrt {3}+c_2 \right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )}{2}+\frac {{\mathrm e}^{-\frac {x}{2}} \left (c_2 \sqrt {3}-c_3 \right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )}{2}+c_1 \,{\mathrm e}^{x}-2 x +c_4 \]

✓ Mathematica. Time used: 0.36 (sec). Leaf size: 70

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

\begin{align*} y(x)&\to \int _1^x\left (e^{K[1]} c_1+e^{-\frac {K[1]}{2}} c_2 \cos \left (\frac {1}{2} \sqrt {3} K[1]\right )+e^{-\frac {K[1]}{2}} c_3 \sin \left (\frac {1}{2} \sqrt {3} K[1]\right )-2\right )dK[1]+c_4 \end{align*}

✓ Sympy. Time used: 0.131 (sec). Leaf size: 41

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

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