29.10.5 problem 271

Internal problem ID [4871]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 271
Date solved : Sunday, March 30, 2025 at 04:08:09 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 39

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

\begin{align*} y &= -\frac {3 x^{2}}{\sqrt {12 x^{3}+9 c_1}} \\ y &= \frac {3 x^{2}}{\sqrt {12 x^{3}+9 c_1}} \\ \end{align*}

✓ Mathematica. Time used: 0.223 (sec). Leaf size: 51

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

\begin{align*} y(x)\to -\frac {x^2}{\sqrt {\frac {4 x^3}{3}+c_1}} \\ y(x)\to \frac {x^2}{\sqrt {\frac {4 x^3}{3}+c_1}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.636 (sec). Leaf size: 46

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

\[ \left [ y{\left (x \right )} = - \sqrt {3} x^{2} \sqrt {\frac {1}{C_{1} + 4 x^{3}}}, \ y{\left (x \right )} = \sqrt {3} x^{2} \sqrt {\frac {1}{C_{1} + 4 x^{3}}}\right ] \]