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Hi, I'm stuck getting the matrix for the laplace transform of the following differential equation:
y''(t) + 7y'(t) + 9y(t) = z'(t) + 2z(t)
So I start out with this by letting x1 = y(t), then x2 = x1' = y'(t) BUT the worked solutions for this question say that:
x2(t) = x1'(t) - z = y'(t) - z ... y'(t) = x2(t) + z
The problem is I cannot figure out WHERE that z comes from? I have never dealt with a differential like this before; all of the other examples are of the form:
[2nd order ODE wrt y(t)] = z(t), could someone please explain how to separate this example up into the x1, x2, form?
y''(t) + 7y'(t) + 9y(t) = z'(t) + 2z(t)
So I start out with this by letting x1 = y(t), then x2 = x1' = y'(t) BUT the worked solutions for this question say that:
x2(t) = x1'(t) - z = y'(t) - z ... y'(t) = x2(t) + z
The problem is I cannot figure out WHERE that z comes from? I have never dealt with a differential like this before; all of the other examples are of the form:
[2nd order ODE wrt y(t)] = z(t), could someone please explain how to separate this example up into the x1, x2, form?
