- #1

- 5

- 0

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

The question is like:

Find the function y

_{1}of t which is the solution of:

9y

^{''}-36y

^{'}-45y=0

with initial conditions y

_{1}(0)=1, y

^{'}

_{1}(0)=0

y

_{1}= ?

Find the function y

_{2}of t which is the solution of:

9y

^{''}-36y

^{'}-45y=0

with initial conditions y

_{2}(0)=0, y

^{'}

_{2}(0)=1

y

_{2}= ?

Find the Wronskian W(t)= W(y

_{1}.y

_{2})

W(t)=?

The way I tried to achieve the problem is to solve the characteristic equation, which is

9r

^{2}-36r-45=0, which gives r

_{1}=5 and r

_{2}=-1; then I consider y

_{1}and y

_{2}are exp(r

_{1}) and exp(r

_{2}) respectively. But it seems my answer is wrong...