56.2.2 problem Ex 2

Internal problem ID [14085]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 9. Variables searated or separable. Page 13
Problem number : Ex 2
Date solved : Thursday, October 02, 2025 at 09:11:09 AM
CAS classification : [_separable]

\begin{align*} \left (1+x \right ) y^{2}-x^{3} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=(1+x)*y(x)^2-x^3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.104 (sec). Leaf size: 29

ode=(1+x)*y[x]^2-x^3*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 x^2}{-2 c_1 x^2+2 x+1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 17

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

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