75.3.6 problem 6

Internal problem ID [19910]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 6
Date solved : Thursday, October 02, 2025 at 05:00:52 PM
CAS classification : [_linear]

\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y&=x^{3} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=x*(-x^2+1)*diff(y(x),x)+(x^2-1)*y(x) = x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\left (\ln \left (x -1\right )+\ln \left (x +1\right )-2 c_1 \right ) x}{2} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 21

ode=x*(1-x^2)*D[y[x],x]+(x^2-1)*y[x]==x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.182 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 + x*(1 - x**2)*Derivative(y(x), x) + (x**2 - 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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