62.12.20 problem Ex 21

Internal problem ID [12795]
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 19. Summary. Page 29
Problem number : Ex 21
Date solved : Monday, March 31, 2025 at 07:07:59 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 33

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

\[ y = \frac {{\mathrm e}^{-3 c_1}}{\sqrt {\frac {{\mathrm e}^{-6 c_1}}{x^{6} \operatorname {LambertW}\left (\frac {{\mathrm e}^{-6 c_1}}{x^{6}}\right )}}\, x^{3}} \]

✓ Mathematica. Time used: 1.514 (sec). Leaf size: 46

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

\begin{align*} y(x)\to -\sqrt {W\left (\frac {e^{2 c_1}}{x^6}\right )} \\ y(x)\to \sqrt {W\left (\frac {e^{2 c_1}}{x^6}\right )} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.720 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {e^{C_{1} - \frac {W\left (\frac {e^{2 C_{1}}}{x^{6}}\right )}{2}}}{x^{3}} \]