15.18.6 problem 6

Internal problem ID [3249]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 6
Date solved : Sunday, March 30, 2025 at 01:25:02 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x y^{\prime \prime }&=x^{2}+1 \end{align*}

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

ode:=x*diff(diff(y(x),x),x) = x^2+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \ln \left (x \right )+\frac {x^{3}}{6}+\left (-1+c_1 \right ) x +c_2 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 25

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

\[ y(x)\to \frac {x^3}{6}+x \log (x)+(-1+c_2) x+c_1 \]

✓ Sympy. Time used: 0.168 (sec). Leaf size: 17

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

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