69.16.19 problem 492

Internal problem ID [18279]
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 : 492
Date solved : Thursday, October 02, 2025 at 03:10:05 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ y = \sin \left (x \right ) c_1 -\cos \left (x \right ) c_2 +2 x +c_3 \]

✓ Mathematica. Time used: 54.937 (sec). Leaf size: 151

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

\begin{align*} y(x)&\to \int _1^x(c_1 \cos (K[1])+c_2 \sin (K[1])+2)dK[1]+c_3\\ y(x)&\to 4 \pi \text {IntegerPart}\left [\frac {x-1}{2 \pi }\right ]+4 \pi \text {frac}\left (\frac {x-1}{2 \pi }\right )+c_2 \left (-\cos \left (2 \pi \text {frac}\left (\frac {x-1}{2 \pi }\right )+1\right )\right )+c_3+c_2 \cos (1)\\ y(x)&\to 4 \pi \text {IntegerPart}\left [\frac {x-1}{2 \pi }\right ]+4 \pi \text {frac}\left (\frac {x-1}{2 \pi }\right )+c_1 \sin \left (2 \pi \text {frac}\left (\frac {x-1}{2 \pi }\right )+1\right )+c_3-c_1 \sin (1) \end{align*}

✓ Sympy. Time used: 0.066 (sec). Leaf size: 17

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

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