67.2.14 problem Problem 1(n)

Internal problem ID [13900]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 1(n)
Date solved : Monday, March 31, 2025 at 08:17:29 AM
CAS classification : [[_3rd_order, _quadrature]]

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

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

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

\[ y = \frac {1}{6} x^{3}+\frac {1}{2} c_1 \,x^{2}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 25

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

\[ y(x)\to \frac {x^3}{6}+c_3 x^2+c_2 x+c_1 \]

✓ Sympy. Time used: 0.061 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + \frac {x^{3}}{6} \]