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## #1 2006-02-23 02:48:04

Loïc
Member
Registered: 2006-02-23
Posts: 2

### differential equation xy"+y'-mxy=0

Does anybody could help me with the following equation:
xy"+y'-mxy=0
or
my=y"+y/x
It comes from the Laplace transform of a problem of heat conduction in polar coordinates.

Thanks

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## #2 2006-02-23 06:51:18

ryos
Member
Registered: 2005-08-04
Posts: 394

### Re: differential equation xy"+y'-mxy=0

What do you need to do to it?

I'm a little rusty on diffEQ (what I've had of them, anyway), but don't you need to integrate both sides? In this case, you'd have to do it twice.

I've also not had multivariable calculus, so I'd need to separate the variables.
So, solving for x, we find that
x = -y′ / (y″ - my)

Integrating both sides gives:
1/2 x² + C = ∫[ -y′ / (y″ - my) ]

The integral on the right evades me. Sorry.

Last edited by ryos (2006-02-23 07:04:19)

El que pega primero pega dos veces.

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## #3 2006-02-23 13:40:10

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: differential equation xy"+y'-mxy=0

In differential equations, you want to find an equation, not a value.  Thus, you are solving for y, not x.

It's been a long time for me as well (ok... 2 months... but still...), I know you can solve any 2nd degree equation (that is solvable) using matricies.  But I don't believe there is any simpiler form for this equation.

How much about diff eq do you know?  Is this a course in it or are you just studying yourself?  Have you used matricies to solve differential equations in the past?

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #4 2006-02-23 17:54:04

Loïc
Member
Registered: 2006-02-23
Posts: 2

### Re: differential equation xy"+y'-mxy=0

I need to solve this equation to find the right temperature profile in a metal plate following a determined heat flow on the surface. I have used computer modeling and I need to confirm the temperature profile by equations.

I did a lot of diff eq about 20 years ago. I have tried different ways I could think about and find in books or internet, but now I need a little help.

I will check for matricies.

Thanks

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