Earth falling into sun problem

1. The problem statement, all variables and given/known data
If Earth stops rotating Sun suddenly , how long would it take for Earth to collide with Sun ?
G = gravitational constant
m_s = 2e11kg
m_e = 6e24kg
where m_s is the mass of the sun and m_e , mass of earth
x = 1au =1.5e11m
2. The attempt at a solution
Gravitational acceleration ,
a = G(m_s + m_e)/x^2

d^x/dt^2 = a
dt = sqrt(1/a).dx
dt = x/sqrt(G(m_s + m_e)) . dx
integrating over x from x = distance between earth and sun to 0
t = x^2/(2*sqrt(G(m_s + m_e)))

The answer i m getting is not right , anyone help me finding out the solution and what i did wrong

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