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Purav S.

Calculus 3

1 week, 5 days ago

# Determine the form to be used for xp when using the method of undetermined coefficients. x'' + 4x' + 5x = 4e?t

Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients. $y^{\prime \prime}-y^{\prime}-2 y=x e^{x} \cos x$

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### Video Transcript

Okay, so here we have a non homogeneous, different cell equation and, ah, we have to write the trial solution for the method of undetermined coefficient. So first of all right, the auxiliary equation for the homogeneous system. So here L square, minus r minus two that is a go to zero now used the quadratic formula to solve the situation. So called it a formalized given by our is equal to negative B plus or minus square root off B squared, minus four, etc. He rented. By the way, your baby is equal to minus one and here, minus one whole square, that is, one is equal to one and C is equal. Do minus two divided by two a and here is equal to one you're for multiplied by two that is eight and one plus eight That is equal. Do nine and square root off nine that is three. So here artistic called one plus three divided by two and Article one minus three, divided by two. So here are is equal to two and R is equal to minus one. So here we have a to really roots. Therefore particular solution is given by Y. C is he called toe? Here s to two weeks. Plus it is two minus X and multiply the constant C one and C two. Right. Okay, so now on the right side of the our function is X multiplied by it is two x Cossacks. So let's assume that our particular solution is in the form off. It is two x cause affects. Plus, it is two eggs. Sign off, X. Right. But your ex is in the multiplication. So here we have to multiply the equation off line. And here, equation off line, which is in the form off X plus b and here used the different coefficients. So here we can you, c and d. So here are C X plus D. So this is the hour form off the particular solution. Right? Thank you.

##### Lily A.

Johns Hopkins University

##### Kristen K.

University of Michigan - Ann Arbor

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