Question

Given the following differential equation: og = Ax + eAt (sin(t) + 2cos(3t)), x ERP and y(t) = e-At x (t). What is it o dogte = sin(t) + 2c08(3t) ody = -2Ae-At æ(t) + sin(t) + 2008(3t) o di = 2 Ae-At ze(t) + sin(t) + 2cos(3t) o date= sin(t) – 2cos(3t)

Please answer this multiple choice question

Answer 1

I am attaching the pictures of solution. Thanks

Ans Given de - Axt A2 (sin (8) + 2 C02(34) & - & - Now [***] * (tv) ***** (615Pemil +(096) A = [(x)66034) H ome ** ** (-A EA!) because of (eat) = a cat] cause

- dy_ě At dx – Axe At dt Now using ①, we can write d = e. At (x + 6+ (Sin (+) + 2 (03 (3*)] - Axe At - Axe At + A++ AX (sin (+) + 2 (03 (34) - Axe 4- = e (sin (A) +2 (as (3*)) dy = sin(4) + 2 Cos (3) L first option is correct.