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Solve the following Laplace transform?

Posted 1 month ago
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Consider the following code:

q- 4 q''[x]- 10 w''''[x]== 0

Boundary Conditions:

w[0]== 0,w[1]== 0
w''[0]== 0,w''[0]== 0

I'm unsure the equation is linear. is it? if I take y as associated with q and w, I still have an issue at least for w that only w'''' is mentioned (x and y are not), so without full analysis I assume it's non-linear. but the Laplace I learned can only be used for linear, and to do that - I think more rules would be needed? Am I right?

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