Question

HELLO

I AM CURRENTLY IN DIFFERENTIAL EQUATIONS

PLEASE EXPLAIN EACH STEP SO I CAN LEARN FROM YOU (I KNOW SOME PEOPLE ONLY CARE ABOUT TEH ANSWER, BUT WILL REALLY APPRECIATE IT) TO SAVE TIME FEEL FREE TO JUST SAY A LAW, THEOREM, OR CONCEPT FOR AN EXPLANATION AND I CAN GO AHEAD AND STUDY IT ON MY OWN.

i REALLY DO READ THESE VERY CAREFULLY AND USE THE COMMENTS OFTEN, SO JUST A LITTLE HEADS UP.

I FIND IT DIFFICULT TO READ HANDWRITTEN STUFF SO IF YOU CAN DO IT ELECTRONICALLY THAT WOULD BE FANTASTIC.

PLEASE TAKE YOUR TIME AND STAY SAFE OUT THERE.

Use method of undetermined coefficients to determine the appropriate form of a par- ticular solution yp(2) of the differential equation: y" + 4y' + 4y = 2xe-24 + 8 sin (2x). (Do NOT solve for the coefficients constants).

Answer 1

bron * +4y'+4y = 2 xe *** +8sin (2x) auxilliary equation is ma +4m+4 = 0 m=-2,-2 yo = (4 +c2x)e-2 The two linearly independent solutions of complementary solution are (x) = eº, y(x)= xerºx The nonhomogeneous part of de is 2xe*** +8 sin (2x) Derivatives of nonhomogeneous part of de are xe 2*, -2*, sin (2x), cos (2x) and are of the form xe-* for the non-negative integer k=1 so y(x)= Ax*e^2* + B sin (2x) +C cos(2x) P