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**2nd order diff Eq with t missing**

I am trying to find y as a function of t

and y'' - y = 0

The two IV given are y(0) = 7, and y(1) = 5 .. Remark: the initial condition involves values at two points.

Well since y = {y,y''} and the independent variable t does not appear, I went about it by setting z = y' and trying to reduce it to a first order DE.

z = dy/dt = y'

z * dz/dy - y = 0

z(dz/dy) = y

Separating the variables and integrating...

zdz = ydy

(z^2)/2 = (y^2)/2 + c

z^2 = (y^2) + C (where C = 2c)

z = sqrt (y^2 + C)

Normally here I would use the IVs to determine C before..however both there is no IV involving y'(t)...

Anyways...

z = sqrt (y^2 + C)

y' = sqrt (y^2 + C)

dy/dt = sqrt (y^2 + C)

dy/sqrt(y^2 + C) = dt

So do I just integrate from here? Isn't this a composite function on the left hand side...so the variable y would appear as well as y^2 ?

How do I solve this problem and get an answer in the form of y(t) = _________________

Any help would be appreciated.