A second ODE problem that bothers me a lot HELP

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The discussion centers on solving a second-order ordinary differential equation (ODE) given by the equation 9y'' - 36y' - 45y = 0. Two specific solutions, y1 and y2, are sought with different initial conditions: y1(0) = 1, y'1(0) = 0 and y2(0) = 0, y'2(0) = 1. The characteristic equation derived from the ODE is 9r² - 36r - 45 = 0, yielding roots r1 = 5 and r2 = -1. The Wronskian W(t) of the two solutions is also requested, indicating the need for further analysis of the linear independence of y1 and y2.

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A second ODE problem that bothers me a lot~~ HELP!

The question is like:
Find the function y1 of t which is the solution of:
9y''-36y'-45y=0
with initial conditions y1(0)=1, y'1(0)=0

y1= ?


Find the function y2 of t which is the solution of:
9y''-36y'-45y=0
with initial conditions y2(0)=0, y'2(0)=1

y2= ?


Find the Wronskian W(t)= W(y1.y2)

W(t)=?

The way I tried to achieve the problem is to solve the characteristic equation, which is
9r2-36r-45=0, which gives r1=5 and r2=-1; then I consider y1 and y2 are exp(r1) and exp(r2) respectively. But it seems my answer is wrong...
 
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never mind, I got it.
 

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