(a) The eigenfunctions of the following eigenvalue problem: X" + XX = 0, X'(0) = X'() = 0 are given by Xn D (A) sin(nz), n= 0, 1,2, 3, .. (C) cos(nz), n = 0, 1, 2,3,. (B) sin(nz), n= 1,2,3,.. (D) cos(nz), n = 1,2, 3, .

Q: A second order Caushy – Euler equation having a solution y(x) = x-cos(4Inx) is O x²y" + 5xy' + 16y =…

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Q: 6. y" + 3y'-2y e-2* [(4+20.x) cos 3x+ (26-32x) sin 3x]

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Q: Find the general solution of (D²-7DD' + 12D'2)Z = sin(x - 2y) + ex-2y

A: This question is from linear partial differential equation.

Q: A. Yp(x) = Ax² + Bx + C, B. Y,(x) = Ae², c. y,(x)= Acos 2x + Bsin 2z D. yp(x) = (Ax +B) cos 2x + (Cx…

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Q: a) m - 1 b) m – 2 Q.8) The characteristic equation for y"" + 3y" – 4y = 0 , is : b) 2' = 32?-4 c) m…

A: To find out the characteristic equation.

Q: 6. Setting æ = cos 0 show that T.(e) = [(- + ivI- =')" + (* - ivī- =')"] n where i = V=1.

A: This immediately follows as a consequence of De Moivres formula which states that e^(it)=cos t + i…

Q: Deduce that if (b) Let a 2 cos 2 and ß = 2 cos 4. Show that a = @ +w4 and B=w² +0³. Find a quadratic…

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Q: (c) Given T" = 6x²y³ – cosx + 5y² – siny + 10x² – e-3x," determine (1) T' = S(T")ax T' = S(T")ay…

A: GivenT"=6x2y2-cos x+5y2-sin y+10x2-e-3xwe know…

Q: 4. The function f(x) = 2r + cos(r) (shown right) is invertible. (a) What is the value of f-(1)?…

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Q: A car costs x wholesale. The price the dealer pays is given by the function s(x) = = x-1 – 200 where…

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Q: Solvecos (2) O a. O b. 2 с. d. y cos Y I - [2 in (2) + co. (:)]* - = 0 dz y sin () = c C = сх ysin…

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

Q: Match the graphs with their parametric equations. I O (a) x=4-t+2, y = ² O (b)x= 2 - 3t, y = √t O…

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Q: The derivative of f (#) cos(-2 a +a - a2 - 2 a +1) is O f (a) = (8 a° – 3 a? +2 a + 2) sin (-8 a + 3…

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Q: 2. Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x + n IN

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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: [Motion in R³] A drone has an initial position of (3,1, 2) and an initial velocity of (-2,5,1). The…

A: Here we can use the following formula to find displacement function: vt=∫at dtst=∫vt dt

Q: 6. Setting æ = cos 0 show that T,(x) = [(r + VI– a²)" + (x – v1- x²)"]

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Q: what is the general solution of y''+4y=cos(2x)

A: Given: y''+4y=cos(2x)

Q: blem 2 Let A > 0 and A + na. y" (t) +X'y (t) =Dan cos (nat) n=1

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Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: 1. Solve the initial value problem on the real line Utt - Uzz = sin x U(x,0) = 0 Ut(x,0): = sin x

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Q: 4. Suppose the following functions are a general solution of: y(4) + azy" + azy" + a13 + a0y = 0…

A: The differential equation is y(4) + a3y''' + a2y'' + a1y' + a0y = 0 We have to find a0, a1, a2 and…

Q: y=(b+x²)* +(1+x°)* ( \3x² +x – c )cos²(4x) y'=? %3D %3D

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Q: 2) y"+y' - 1 = 3 cos(x)

A: 2.

Q: Can you explain how all A B C D terms are calculated

A: Solution of the given question is like as

Q: 3. Solve y' + cos(r)y = 2 cos z subject to the initial condition that y() = 2.

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Q: 5. Find ALL degree solution of 3sin 0 + 3 = 2 cos' 0.

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Q: Slve the Following initl Value Problems s- a) V+4Y=20 (y=2), b)y'= 2(V-1) tanhx (YCO) =4), c)Y'+3Y=…

A: Disclaimer:  Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Classify the zeroes (according to order) and isolated singularities of (2² - 1)e¹/² cos (TZ) (z + 2)…

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Q: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

A: Given

Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

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Q: We consider the following 27-periodic function f given by S0, if -n 1. 3- Deduce the Real Fourier…

A: NOTE: Hi! Thank you for your question. As per the honor code we are allowed to answer three subparts…

Q: Find dy/dt. 9) y = cos (rt - 20) A) -7n sinº(nt – 20) C) 7 cos (zt - 20) B) -7n cos(nt – 20) sin(7tt…

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