58.1.9 problem 9

Internal problem ID [9080]
Book : Second order enumerated odes
Section : section 1
Problem number : 9
Date solved : Wednesday, March 05, 2025 at 07:19:15 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \frac {1}{6} x^{3}+c_{1} x +c_{2} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.071 (sec). Leaf size: 12

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

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