75.16.43 problem 516

Internal problem ID [16937]
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 : 516
Date solved : Thursday, March 13, 2025 at 09:00:45 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=2 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=3*diff(diff(diff(diff(y(x),x),x),x),x)+diff(diff(diff(y(x),x),x),x) = 2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}}{3}+\frac {c_{2} x^{2}}{2}-27 \,{\mathrm e}^{-\frac {x}{3}} c_{1} +c_{3} x +c_4 \]

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 36

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

\[ y(x)\to \frac {x^3}{3}+c_4 x^2+c_3 x-27 c_1 e^{-x/3}+c_2 \]

✓ Sympy. Time used: 0.100 (sec). Leaf size: 24

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

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