8.6.19 problem 19

Internal problem ID [789]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 19
Date solved : Tuesday, March 04, 2025 at 11:48:41 AM
CAS classification : [_separable]

\begin{align*} 3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=3*x^5*y(x)^2+x^3*diff(y(x),x) = 2*y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{2}}{x^{5}+c_1 \,x^{2}+1} \]

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 28

ode=3*x^5*y[x]^2+x^3*D[y[x],x] == 2*y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {x^2}{x^5-c_1 x^2+1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.197 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**5*y(x)**2 + x**3*Derivative(y(x), x) - 2*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{2}}{C_{1} x^{2} + x^{5} + 1} \]