Question

dy/dx = y/(x+y^2cos y)

Answer 1

This problem really belongs in mathematics, but it's so good I'll try and answer it here.

It's easiest to think of this as

dx/dy = (x + y^2 cos y)/y = x/y + y cos y
or
x' - (1/y)x = y cos y

Given that form, you can solve using standard first-order ODE techniques.

Answer 2

i.e., x(y) = Ay + By.sin y

Now you need to invert that equation. As you can see, the inverse in general won't be pretty.

Answer 3

thanks dude

Answer 4

invert the already inverted one?

Answer 5

I mean you'd need to find the inverse function of x(y).

Answer 6

please explain

Answer 7

Your original equation implicitly asks for a solution
y = f(x),
y as a function of x.

The solution I've provided gives x as a function of y.

Hence if you actually need y = f(x), then you'll need to find the inverse function of
x = g(y) = Ay + By.sin y

The inverse function of g will be the function f.
\[ f^{-1} = g \]

Answer 8

Thanks again homie