Question

Solve the differential equation dy/dx = (x-2) / (y-2)

Answer 1

y = 2 ±
`√(x^2 - 4x + 4 + C)`

Explanation:

Solve using separable equations

First put x and dx on the same side and do the same for y

(y-2)dy = (x-2)dx

Now you can integrate

`(x^2)/(2) +2x + C1 = (y^2)/(2) +2y\\` + C1

Now we depending on how what ur instructor wants you may need to give exact solutions. We can do this by solving he quadratic equation for Y

Doing this you get:

y = 2 ±
`√(x^2 - 4x + 4 + C)`

Note C's were simplified.