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
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.
i ran into more trouble doing this problem.
i have no idea whether my answer is right.
transformed equations as in earlier post
Multiply equation 1 by to remove the on the RHS.
Multiply equation 2 by s to remove the 's' on the RHS.
equation 1' & 2' commonly factorized in terms of X
To eliminate X from the pair of equations; eqn 2' is multiplied by (-s-1)
After further simplification
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
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.