Exact Ordinary Differential Equation

syms y(x)
ode=y*(1-x^2)*(diff(y))== ((x*y^2)-(cos(x)*sin(x)))
sol=dsolve(ode)
 
ode(x) =
 
-y(x)*(x^2 - 1)*diff(y(x), x) == x*y(x)^2 - cos(x)*sin(x)
 
 
sol =
 
 ((C1 - cos(x)^2)*(x - 1)*(x + 1))^(1/2)/(x^2 - 1)
-((C1 - cos(x)^2)*(x - 1)*(x + 1))^(1/2)/(x^2 - 1)

Did I properly tranlate the problem below correctly using the right syntax and operations ? Can you please check my code, is it correct ?

Answer 1

[Samuel Brewton]

I just ran it through and got the same solution so it seems to check out.

Answer 2

[Lakshmi]

dx