Diff-EQ HW: f(A)=f(B)=0, f’’(x)+f’(x)=f(x) for all real numbers in [A,B], find f(x)

[yvarou]

Diff-EQ HW: f(A)=f(B)=0, f’’(x)+f’(x)=f(x) for all real numbers in [A,B], find f(x)

Hi guys, first post

Can anyone please help with the following problem?

We have a function f in [A,B]. we know that:
1) f(A)=f(B)=0
2) f’’(x)+f’(x)=f(x) for all real numbers in [A,B]

We need to identify function f.

Many thanks in advance!

 

[Deleted member 4993]

Hi guys, first post

Can anyone please help with the following problem?

We have a function f in [A,B]. we know that:
1) f(A)=f(B)=0
2) f’’(x)+f’(x)=f(x) for all real numbers in [A,B]

We need to identify function f.

Many thanks in advance!

This is a linear second order homogeneous ODE - which can also be written as:

y" + y' - y = 0

What have you been taught about 2nd order ODE?

Exactly where are you stuck?

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

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