83.2.5 problem 1 (e)

Internal problem ID [21916]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. III at page 35
Problem number : 1 (e)
Date solved : Thursday, October 02, 2025 at 08:09:33 PM
CAS classification : [_quadrature]

\begin{align*} x^{3} y^{\prime }-x^{3}&=1 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 12

ode:=x^3*diff(y(x),x)-x^3 = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x -\frac {1}{2 x^{2}}+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to -\frac {1}{2 x^2}+x+c_1 \end{align*}

✓ Sympy. Time used: 0.158 (sec). Leaf size: 12

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

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