Differential equations - 2nd order homogenous eq'n w/ unknown

Given that the equation
t d^2y/dt^2 - (1+3t) dy/dt + 3y = 0. has a solution of the form e^ct, for some constant c, find the general solution (The answer is y(t) = c1(1+3t) + c2e^(3t)

Edit: I finished this question as i figured it out. but when i come down to the last step, i get this
y1(t) = e^3t
y2(t) = -1/3t - 1/9

y(t) = c1y1(t) + c2y2(t)
y(t) = c1e^3t + c2(-1/3t-1/9)
y(t) = c1e^3t + -1/9c2(3t+1)

can i bet c3 = -1/9c2?
so it's
y(t) = c1e^3t + c3(3t+1)

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I havn't done a question like this, so I don't know where to start. should i divide everything by t and do reduction of order?

Why divide by t?

Are you familiar with how the reduction of order method woks? This site should help
http://tutorial.math.lamar.edu/AllBrowsers/3401/ReductionofOrder.asp [Broken]

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sorry i figured out how to do it,
can u confirm whether i am allowed to do the last step? i don't see why not but just incase

can u confirm whether i am allowed to do the last step? i don't see why not but just incase

Yes, it's right.