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If given the differential equation *y''-4y'+4y=e ^{t}*, is there a way to solve it for possible solutions?

I have been working questions that provide possible solutions and I need to determine if they are solutions to the differential equation, but what about starting with the differential equation itself and finding a solution. Is it possible?

If so, can you provide one example that starts with the given differential equation, *y''-4y'+4y=e ^{t}*, and arrives at a solution?

If not, can you explain why not?

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