Question

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

Answer 1

Answer:

y = 2 ± $\sqrt{x^2 - 4x + 4 + C}$

Step-by-step 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

$\frac{x^2}{2} +2x + C1 = \frac{y^2}{2} +2y$ + 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 ± $\sqrt{x^2 - 4x + 4 + C}$

Note C's were simplified.