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Hello,

Working through some reduction of order problems. I'm not sure about why the structure of a particular solution is assumed. Here's what I mean:

Given y"-4y = 2 and a known solution is e^-2x, use reduction of order to find a second solution and a particular solution.

Using a formula, the second solution is found quite easily to be y= ce^2x. But the particular solution is assumed to be of the form y = Ax + B. Taking a few derivatives and substituting yields a particular solution of y = -1/2.

But why do we assume the particular solution is of the form y = Ax + B? Thanks in advance,

Lee

Working through some reduction of order problems. I'm not sure about why the structure of a particular solution is assumed. Here's what I mean:

Given y"-4y = 2 and a known solution is e^-2x, use reduction of order to find a second solution and a particular solution.

Using a formula, the second solution is found quite easily to be y= ce^2x. But the particular solution is assumed to be of the form y = Ax + B. Taking a few derivatives and substituting yields a particular solution of y = -1/2.

But why do we assume the particular solution is of the form y = Ax + B? Thanks in advance,

Lee

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