49.1.3 problem 1 (d)

Internal problem ID [7582]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.3 Introduction– Linear equations of First Order. Page 38
Problem number : 1 (d)
Date solved : Wednesday, March 05, 2025 at 04:46:59 AM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=diff(diff(diff(y(x),x),x),x) = x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{60} x^{5}+\frac {1}{2} c_{1} x^{2}+c_{2} x +c_3 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 25

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

\[ y(x)\to \frac {x^5}{60}+c_3 x^2+c_2 x+c_1 \]

✓ Sympy. Time used: 0.106 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + \frac {x^{5}}{60} \]