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boneill3
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Homework Statement
Hi Guy's
Let V be the set of functions [itex]f:R\rightarrowR[/itex]which solve the differential equation:
[itex]\frac{d^2y}{dx^2}=y[/itex]
Show that [itex]e_1:R\rightarrow R, x \rightarrow e^x[/itex] and [itex]e_2:R\rightarrow R, x\rightarrow cosh(x)[/itex]
Comprise a basis for V.
Homework Equations
The Attempt at a Solution
I have not done 2nd order differential equations and I was wondering if some one might give me a hint to a particular solution vector.
I know I need to prove that [itex] e^x [/itex] and [itex] cosh(x) [/itex] are linear independant to be a basis, but I need to show that any solution vector can be generated by them.
with the natural log we can't take the log of zero so when can the vector equal zero?