# Laplace Transform of an equation with more than one variable

1. Jan 9, 2009

### Aeana

Hey guys, I'm really struggling with an equation that I have to use for a piece of coursework. I think I'm missing something really basic but I can't seem to get past it and wondered if somebody else could help.

I want to know if it's possible to find the Laplace transform of the following:

du/dt=-0.0291*u+0.0629*w-32*theta+(0.2/m)*deltaT

I've tried everything I can think of including taking the Laplace transform of each variable and then adding them together at the end which I don't think works. I've searched everywhere I can think of for an answer to my problem but I've found nothing.

Can somebody please help me?

2. Jan 9, 2009

### HallsofIvy

Staff Emeritus
Are you saying that u and w are independent variables? Then one equation is simply not enough to determine two variables. If you had two equations, then you could take the Laplace transform of both sides of both equations to get two algebraic equations in the Laplace transforms of u and w.

Assuming that the theta and deltaT are constants, taking the Laplace transform of both sides of this equation, and writing U(s) and W(s) for the transforms of u(t) and w(t), respectively,
sU(x)- u(0)= -0.0291U(s)+ 0.0629W(s)+ ((0.2/m)deltaT- 32theta)/s

Last edited: Jan 9, 2009
3. Jan 9, 2009

### Aeana

Thanks for replying HallsofIvy. u and w are independent variables yes, they are derived from other equations which are computed in simulink. However to be able to compute the values for u,w,etc. I must know the transfer function for the equation mentioned previously. It's very messy.

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