32.10.5 problem Exercise 35.5, page 504

Internal problem ID [5999]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.5, page 504
Date solved : Sunday, March 30, 2025 at 10:29:29 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.282 (sec). Leaf size: 14

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

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