# Partial Differential Equation

1. Nov 21, 2006

### EDerkatch

x(δu/δx)-(1/2)y(δu/δy)=0

By first looking for a separable solution of the form u(x, y)=X(x)Y(y), find the general solution of the equation given above.

Determine the u(x,y) which satisfies the boundary condition u(1,y)=1+siny

For the separable form I have u(x, y)=A(x^c)(y^2c), could someone please show me how to do the rest of it.

Thank you.

2. Nov 21, 2006

### arildno

Write sin(y) as a power series.

3. Nov 21, 2006

### arildno

Each choice of c gives you a solution of your diff.eq.
Since your diff.eq is linear, a sum of such solutions is also a solution of your diff.eq.

4. Nov 21, 2006

### EDerkatch

How do I get from u(x, y)=A(x^c)(y^2c) to the general solution?

Thank you.

5. Nov 21, 2006

### arildno

All right:
A series solution of your diff.eq is:
$$u(x,y)=\sum_{n=1}^{\infty}A_{n}x^{c_{n}}y^{2c_{n}}$$,
whereby follows:
$$u(1,y)=\sum_{n=1}^{\infty}A_{n}y^{2c_{n}}$$
and $A_{n},c_{n}$ are constants.

Now, how can you fit this expression for u(1,y) to the given boundary condition?

6. Nov 21, 2006

### EDerkatch

7. Nov 21, 2006

### arildno

Well, use my first hint in post 2.

8. Nov 21, 2006

### EDerkatch

Ok if you could please show me the COMPLETE working I would really appreciate it... Thank you.

9. Nov 21, 2006

### EDerkatch

Ok if you could please show me the COMPLETE working I would really appreciate it... Thank you.

10. Nov 21, 2006

### arildno

Do you know what a power series is?

11. Nov 21, 2006

### EDerkatch

Yes lol, I just can't do this question, could you please show me the working for it... In fact can you do it yourself?

12. Nov 21, 2006

### HallsofIvy

If you are not capable of doing basic algebra, you should not be attempting partial differential equations!

(Yes, I can do it myself! That's not really the point is it? You have been told exactly HOW to solve your equation, yet you have not even TRIED to apply what you have been told.)

13. Nov 22, 2006

### arildno

That's it. I'm out of here. It is long since I've met a more ungrateful and lazy f*ckhead on PF as you.