Its 2:30am, my maths has to be handed in in 9 hours and 30 minutes, I have half a cup of coffee, its dark and I'm wearing sunglasses. Lets go.

1. Solve the following first order ODE's:

i) x(dy/dx)+3y=x^2       (x>0)

ii) dy/dx - 2xy=x

iii) dy/dt=(t^2)y

iv) x^2(dy/dx)=x^2+3xy+y^2         (x>0)

When I was a kid we had to cheat the hard way....by looking in the back of the book or stealing the answers out of the teacher's desk. You kids have it too easy today.

Ah shit... I have forgotten my A-Level Maths now that I am in Uni!

@ super

yep

No one so far ? But VGC usually loves maths...

I'm ashamed to say, but I've completely forgotten how to solve Ordinary Differential Equations...

this =(

I shant do your maths for you. The point of homework is to learn, not to get the right answers.

That said, I can try to help you to learn :)

iii is best solved by using an integrating factor
http://en.wikipedia.org/wiki/Integrating_factor

The basic steps should be
1 Put the equation in the form
dy/dt + p(t)y = g(t)

2 multiply each of these terms by an as yet unknown term u(t)

3 Write out a value for u(t) that is recognised as the derivative of a fairly simple expression
(you will need the identity that
d [u(t)y] / dt = u(t) dy/dt + du(t)/dt y

By using that, I determined that
du(t)/dt = -t^2 . u(t)

4 rearrange this to get all the u(t) terms on one side, and use standard integrals to determine u(t) (you should get a multiplicative constant, just let it equal 1)

5 Plug your value for u(t) back into the first equation that used u(t)

6 integrate both these sides, remembering to put a constant of integration +c on the right hand side

7 rearrange to get y on its own

My answer was y = e^((t^3)/3)

I shall have a look at the others, and if you get stuck give me a yell

Aren't there any Asian kids in your class you can brown nose? :P

I still can't get ii) and iv) damn it. This should be easy! whats happening

@okey

lol xD