Question

Given `ye^x - x - y^2 = 0` calculate `dy/dx` ?

Answer 1

`(dy)/(dx) = ( 1-e^x y)/(e^x - 2 y)`

Explanation:

Calling `f(x,y) = ye^x - x - y^2 = 0`

we have

`(dy)/(dx) = - f_x/(f_y) = -( e^x y-1)/(e^x - 2 y)`