em # 1 1: Check which one of the following functions is a solution to the di ffe

Question

em # 1 1: Check which one of the following functions is a solution to the di fferential equation y y sin x (A)(cos x + x sin x) (B)(er-cos x) (C)(er-sin x) (D).(sin x-rcos x) (E)ter + cos x) (F) (sin x + x cos x) Problem #11: Just Save Submit Problem #11 for Grading tem t # Your Answer Your Mark: 0/2X blem # 12: For what two values of r does the function y err satisfy the differential equation y" + 6y' + 9y = 0 ? If there is only one value of r then enter it twice, separated with a comma (e.g., 12,12). Problem # 1 2 : Just Save Submit Prob #12 for Grading Problem #12 Your Answer: Your Mark: roblem # 13: By inspecting the following differential equation and its properties, determine which of the given graphs could b

Explanation / Answer

11. y" -y = sin x

Let y= A sin (x) + B cos(x)

y'= A cos(x)-B sin(x)

y" = -A sin (x) -B cos(x)

-A sin (x) -B cos(x)- Asin (x) -B cos(x) = sin x

-2A=1, -2B=0

A=-1/2

B=0

Characteristic equation

t2-1=0

t=-1 ,1

y=c1e-x+c2ex-(1/2) sin x

Correct option is C

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