75.16.19 problem 492

Internal problem ID [16921]
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 : Monday, March 31, 2025 at 03:35:35 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: 60.008 (sec). Leaf size: 29

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

\[ y(x)\to \int _1^x(c_1 \cos (K[1])+c_2 \sin (K[1])+2)dK[1]+c_3 \]

✓ Sympy. Time used: 0.121 (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)
 

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