Question

this is a differential equation question

please solve them with steps and details also, make sure it is correct

4. (7 points) Consider the following system of differential equations, solve it using both the direct method and the Decoupling Method, and compare your results from both methods. 3.x - 2y y = -2 + y + 32

Answer 1

First find the eigen values and then corresponding eigen vectors to find the solution.
Ans عدد :ای لالالا 2 الا لا O 7 Iced 3 2 و | - ولله -صل - 3 - | (3) - + + 2 = 6 :دد(درم -م2م) ج-3) ح=((2-1 / 8-(حمام) -3 .. ( ( (مدن) - 22

Date لكم ج -2 -م-3 2 رد •| 0 R3+ IR 2 6 | C رX 0 ( ه2 دحيلا و يک - وته 0 2 0 علا الا - | R2 - Ra-R, Ry - Rz +R, 2 D 0 0 R X-) Rz 0 * Xa م حالاته اده ها لكحد XX / Spic

d=3 X2 H x3 R₂ - R₂ + Rz 0 x a X3 Rz x Xx 13 R Rz - -3 - 2 o 0 3x = 0 • 2 = 0 let X=0 Xt e ter i 2x e st 3X