Question

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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. T 3r - 2y y -x+y+32

Answer 1

Given 33.ay -01-1 y 32 Decoupling 3 > n y ch 3 2 2 Eigen vallies 3-8 O o.8 3-8 o o - ) -11-6125-0) -5(13-5)?.0) 5) 5(8-3)? * 25.6 2 -) S : 1 1,2,3 si ai 0 2 .2 a 2 1 С» 2 T! 0 29, za2 ai a azt 293 - -2 T// vo 2 a. 292 > IN > & a3

O 3 0 0 an an 0 {p be any real values Set that Penow 5,7 + We Soln 3 37 е x P * + 2c, é? 6 Cze 2A P. e 3t z Cze 2A Direct method of n is in the See e + t Se 34 So let b₂e2t a et 2031 y As we can differentiation linear form It must be in the form combination of get & be 2 deut de att 6 e 24 + dae ut 2- a ett 2b, e? + 36, e3t 4d,eht are 2b2e24 3-4 2bze 27 t 3034 + 2 aze 20 + ot 3lge cs, + udget e 3* + udze 24 at 3C3 4t aze 21

Criren & y 262 0..4d, -- 3n.ry 1 na >> 2. 39,- 292 36, 262 30 - 202 ad, 3d, -ada d, nd, 36, ndyt 32 -a, taz 393 b. + b2 + 363 $9,975 - ag0 262 any 263 tako Value {a} 363 udu -G & C2 + 30₃ -d, a da t 3d, dz Si the end have n t + b, et + + bi Y a, e 3t bie? 21 9.0 If compare eq with Both exactly the same.