Using the Laplace transform, find the functions x(t) and y(t) that satisfy

x=y=0 at t=0 and

dx/dt + 2(dy/dt) + x = t

-dx/dt - dy/dt + y =1

Printable View

- Apr 28th 2010, 02:19 AMKbotzSystem of DE's: Laplace transfomation
Using the Laplace transform, find the functions x(t) and y(t) that satisfy

x=y=0 at t=0 and

dx/dt + 2(dy/dt) + x = t

-dx/dt - dy/dt + y =1 - Apr 28th 2010, 06:02 AMmr fantastic
- Apr 28th 2010, 11:23 AMKbotz
i transformed each one of the variables.

so for the 1st equation i got

sX+2sY = 1/s^2 ......................... eq 3

and transformation of the second equation

-sX-sY = 1/s.............................. eq 4

then eliminated X from both equations by multiplying (eq 3) by -1, and taking eq 4 from it.

Then made Y the subject

Y = 1+s/s^3

I want to know if the previous steps are right, and the approach to the problem.

Thanks Fantastic. - Apr 28th 2010, 07:39 PMmr fantastic
- Apr 28th 2010, 09:13 PMKbotz
oh right, thanks

i will work on it from here and post back if i need more help!

thanks again for the heads up mr.fantastic! - May 2nd 2010, 10:35 PMKbotz
hey,

i ran into more trouble doing this problem.

i have no idea whether my answer is right.

**transformed equations as in earlier post**eqn (1)

eqn (2)

**Multiply equation 1 by to remove the on the RHS.**

**eqn (1')**

Multiply equation 2 by s to remove the 's' on the RHS.

**eqn (2')**

equation 1' & 2' commonly factorized in terms of X

....**eqn(1')**

.....**eqn(2')**

**To eliminate X from the pair of equations; eqn 2' is multiplied by (-s-1)**After further simplification

.....**eqn(2'')**

**Now X can be eliminated, so subtract eqn (2'') from eqn (1')**

*I don't know if this is right***, after subtraction i got:**

**Make Y the subject**

, which is the same as

**Now using partial fractions**

cross multiply

**when****s = 0, B=0 and A = 2**

then when s =1, substitute in A =2 to find out B

**Taking the inverse laplace transform of the partial fraction:**

Please check my steps, i hope it makes sense.

And i have no idea how to get**x(t),**i keep coming to really complex equations. - May 3rd 2010, 01:48 AMmr fantastic
- May 3rd 2010, 01:54 AMKbotz
- May 3rd 2010, 02:04 AMKbotz
oh right, my bad!

i can't subtract properly

0-(-s) = s

not -s. lol - May 3rd 2010, 02:07 AMmr fantastic
- May 3rd 2010, 02:56 AMKbotz
yeah figured them both out!

and got the final transforms too!

i was on the right track for x(t) from the start!

but cheers again!