75.16.20 problem 493

Internal problem ID [16914]
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 : 493
Date solved : Thursday, March 13, 2025 at 09:00:23 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.076 (sec). Leaf size: 19

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

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