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**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)

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)

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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