23.1.366 problem 351

Internal problem ID [4973]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 351
Date solved : Tuesday, September 30, 2025 at 09:06:38 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 29

ode=x^3*D[y[x],x]==(1+x)*y[x]^2; 
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: 0.123 (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)
 

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