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.

-2r 1. Which one of the following options could play the role of fundamental set of solutions for the differential equation: y" + 2y" + 9y' + 18y = 0? (a) {e ", cos 3x, sin 3x, cos 3x – sin 3x} (b) {cos 3x, sin 3x, cos 3x – sin 3x} (e) {e=21, cos 3x, sin 3x} (d) {e-21, cos 3x}

Answer 1

0 Given differential equation is 0 - y" + 2y" + 9 y' +18 y 0 first change the equation into operator form we let d then. dx . = DY, y" - Dly, y" = 2y Putting these values in equation ③ D3y + 2 Day +9DY + 18 y + (D3 + 2D2 + 9 D +18) y = 0 Now, the auxiliary equation es. 2 a +20° +92 +18 =0 { .put а at place of D} (+2) 672 +9) = 0 2+2 22-2 2 = + 3 i 2? +9 -0 so tundamental set of solutions is. { é 2x , Cosur, sinar } CS op tonith (C) ts. correct.