8.5.41 problem 41

Internal problem ID [769]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 41
Date solved : Saturday, March 29, 2025 at 10:21:35 PM
CAS classification : [_exact, _rational]

\begin{align*} \frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}+\frac {2 y}{x^{3}}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 35

ode:=2*x/y(x)-3*y(x)^2/x^4+(-x^2/y(x)^2+1/y(x)^(1/2)+2*y(x)/x^3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {2 y^{{3}/{2}} x^{3}+c_1 \,x^{3} y+x^{5}+y^{3}}{x^{3} y} = 0 \]

✗ Mathematica

ode=2*x/y[x]-3*y[x]^2/x^4+(-x^2/y[x]^2+1/y[x]^(1/2)+2*y[x]/x^3)*D[y[x],x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x/y(x) + (-x**2/y(x)**2 + 1/sqrt(y(x)) + 2*y(x)/x**3)*Derivative(y(x), x) - 3*y(x)**2/x**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out