19. Solve dy/dx={xy+3x-y-3}/{xy-2x+4y-8} by separable method.

To solve the differential equation

we can rearrange the terms in the numerator and denominator to get:

Now we can use the method of separation of variables by multiplying both sides by the denominator and then separating the variables as follows:

By rearranging with respect to variables we get:

Integrating both sides with respect to their respective variables, we obtain:

Now we can simplify this expression, therefore, we have:

Therefore, the general solution to the differential equation is given by:

where is an arbitrary constant.

Now, we can simplify this expression