75.16.40 problem 513

Internal problem ID [16942]
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 : 513
Date solved : Monday, March 31, 2025 at 03:36:01 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{2}}{2}+{\mathrm e}^{-x} c_1 +c_2 x +c_3 \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 27

ode=D[y[x],{x,3}]+D[y[x],{x,2}]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.074 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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