It depends on the type of equation. There are lots of different ways to do it.

2. raja23

yes, i'm just trying to refresh my knowledge on it. Do you know of any good source where I can see some examples?

For Differential Equations after calculus or for derivatives?

4. raja23

well I guess it would be after calculus but this is the eqn \[dy/dt=-5y^2+3uy+6u^2\]

There is no way to make that linear. It's a quadratic and polynomials of degrees other than one cannot be changed to become linear.

6. raja23

yikes well too bad I have it as an assignment question :P thanks though

Also, are you sure all the variables are right? Because right now you have a diff.eq in which you're deriving with respect to a variable that isn't on the right side of your equation...

8. raja23

dy/dt? there are ys on the right side?

Yes but the equation is taking the derivative with respect to t. It would be the same as if I had equation y = x^2 + xy + y^2 and then took the derivative with respect to t I would get dy/dt = 0 because I have no variables with t in them, therefore everything else is considered a constant. Since you don't have t on the right side anymore, I'm assuming that the original equation was something like (−5y^2+3uy+6u^2)*t Otherwise, the right side would be dy/du

10. raja23

good catch but the question given has dy/dt though, i'm guessing prof made a mistake :)

11. raja23

sorry just realized both u and y are a function of t, should be y(t) and u(t)