29.12.27 problem 346

Internal problem ID [4946]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 346
Date solved : Sunday, March 30, 2025 at 04:17:32 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.14 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.208 (sec). Leaf size: 10

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

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