Find the solution of the given initial value problem: y"" + y' = sec(t), y(0) = 11, y′(0) = 5, y'(0) = −6. y(t) = = 5 + 6 cos(t) + 5 sin(t) + In|sec(t) + tan(t)|— t cos(t) + sin(t) + In cos(t)| X

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A: Find the general solution of (a) Using undetermined coefficients.(b) Using variation of parameters.

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Q: y" (t) - y(t) = 4 cos(t) ;y(0) +0 , y'(0)=1.

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A: Given differential equation is yxcosyx-xysinyx+cosyxdydx=0       (1) Simplifying (1), we get…

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Q: where O O O y(t) = (f-cost)-(1)[(1 − 6) - cos(t = 6)] + 6 sint +4 cost - sint) ([(-6)-sin(t-6)] + 6…

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Q: After applying variation of parameters to y " +y = sec(x), the following equations are obtained c{…

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Q: y (3, 4) sin(0) = %3D cos(0) = tan(0) = csc(0): sec(0) : cot(0) = %3!

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Q: Find f. f(0) = f "(0) = sin(0) + cos(0), f(0) = 1, f(0) = 1, f'(0) = 3

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A: see below the answer and explanation

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A: this is a linear differential equation. solve it using integrating factors.

Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

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A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: QUESTION 6 Let fo(x) = nx2 +5 for neN and x ER 4n +3 1. Show that (f.(x)) converges uniformly on [ -…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: This question is related to derivative, we will solve it using given information.

Q: Solve the equation y" +4y= S(t-4π), y(0) = 1/2, y'(0)=0 a. )= = cos(2t) + sin(2(t − 4π)µ(t − 4π)

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Q: (d) If x y/1-y², find

A: Solving question1 for other question repost.

Q: Find the solution of with y(0) = 9 and y'(0) = 7. Y y" + 3y = 126 sin(3t) + 162 cos(3t)

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Q: 4. Let 0 ‡ b, c E Rn and define A = be E Rnxn. Show that (a) R(A) = span{b}, (b) N(A) = {x ≤ R" |…

A: (a) We are given that A = bcT                    where, c ∈ Rn     So, R(A) = { Ax : x ∈ Rn×1 }…