Example 3: Solve .

Solution: We can solve this equation by separating the variables as follows. and this can be factored as , and finally we are able to separate variables by writting the original equation as . At this point we use Maple to finish the job

> int(1/(2-y),y)=int(x^2-x-1,x);

We can write this solution in explicit form using Maple command solve by solving the previcolor=#000000>by solving the previous expression in .

> solve(%,y);

To check that this is indeed a solution of the original problem we first make the previous expression as a function of . Remember this is done using Mapple command unapply together with Maple short way of denoting previous expressions, that is together with % .

> y:=unapply(%,x);

Now we plug this in the original equation and use Maple command simplify to check that this is indeed a solution.

> simplify(diff(y(x),x)-(2*x^2+y(x)-x^2*y(x)+x*y(x)-2*x-2));