Can substitution solve the de sitter universe problem?

[p.p]

rho=0, lambda>0 and k=1 with the initial condition R(0) = sqrt(3/lambda), the solution is
R(t) = sqrt(3/lambda)cosh*(sqrt(lambda/3)*ct)

This the the de sitter universe, however i am having problems finding a way around how to solve it from the Friedmann equation:

dR/sqrt((lambda*R^2/3)-1) = ct


P

 

[phsopher]

Use a substitution

$$\frac{\Lambda R^2}{3} = \cosh^2\phi$$