Question

(2y - 1/ x + cos (3x) ) (dy/dx) + y/x^2 - 4x^3 + 3y sen 3x = 0 Exact equations ?

Answer 1

Not exact

Explanation:

If it is exact then:

`(2y - 1/ x + cos 3x ) dy + (y/x^2 - 4x^3 + 3y sin 3x) dx = 0`

Which can be thought of as:

`d[f(x,y) = C] = f_y \ dy + f_x \ dx = 0`

If so, the mixed partials should be equal:

• `f_(yx) = 1/x^2 color(red)(-) 3 sin 3x`

• `f_(xy) = 1/x^2 color(red)(+) 3 sin 3x`

So this is not exact