You can solve this by taking the first and second derivatives of each of the possible solutions, and then plugging them into the differential equation to see if you really get 0. The answer turns out to be the second function:

`y=e^(-4x)`

`y'=-4e^(-4x)`

`y''=16 e^(-4x)`

Plugging these into the differential...

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You can solve this by taking the first and second derivatives of each of the possible solutions, and then plugging them into the differential equation to see if you really get 0. The answer turns out to be the second function:

`y=e^(-4x)`

`y'=-4e^(-4x)`

`y''=16 e^(-4x)`

Plugging these into the differential equation, we have:

`16e^(-4x) + 7(-4)e^(-4x)+12e^(-4x) = 0`

That is, this really does solve your ode.

**Thus the correct solution is #2**