# If given the differential equation y''-4y'+4y=et, 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=et, and arrives at a solution?If not, can you explain why not?

Question

If given the differential equation y''-4y'+4y=et, 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=et, and arrives at a solution?

If not, can you explain why not?

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Step 1

we are given a differential equation as

Step 2

Homogenous Solution:

we can set right =0

and then we can find homogenous solution

Step 3

Particular Solution:

Let's assume particular so...

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### Differential Equations 