# Q15. Onlys all the three subparts Transcribed Image Text: 15. Determine if the given functions are linearly dependent or independent. (Prove

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y” + 4y – 5y = 3sin 2r 17. Find an Annilator Q(D) for the given functions: a. F(x) – 3xe” c. F(x) = e”+x b. F(x) = 10 d. F(x) = – 6e” cos(5x) e. F(x) = 1+7x-x f. F(x) = sin x+ x |

Q15. Onlys all the three subparts Transcribed Image Text: 15. Determine if the given functions are linearly dependent or independent. (Prove your answers)

a. fe”,3x} b. (-9x’ +1,3x c. 1-2sin’ x,cos 2.x}

16. Find the general solution to the given differential equations:

a. (D’ + 2D+10) y = o

b. [D(D +4)]y =0

c. [(D +16)ly = 4cos.x

d. y” -y – 2y = Se

e. y” + 4y – 5y = 3sin 2r

17. Find an Annilator Q(D) for the given functions:

a. F(x) – 3xe”

c. F(x) = e”+x

b. F(x) = 10

d. F(x) = – 6e” cos(5x)

e. F(x) = 1+7x-x

f. F(x) = sin x+ x

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