2ä + 2i + x =1 with x(0) = 0 and ¿(0) = 2 Answer: x(t) = 1+ 3e-0.5t sin 0.5t – e-0.5t cos 0.5t

Q: - ) s2 – 4 2s+6 What is L -2 cos 2t-3 sin 2t A.

A: find the inverse laplace transform of L-1-2s+6s2-4 we can write the function as…

Q: 7.Obtain the general solution using the method of undetermined coefficients. a. (D² + D)y = - cos x…

A: First we put auxiliary equation D2+D=0 then solve it.

Q: 8. (a) 2e' (cos 3t – 3 sin 3t) (b) 3e-2 (sinh 2t – 2 cosh 2t)

A: Given functions: (a) 2etcos3t-3sin3t (b) 3e-2tsinh2t-2cosh2t   We know that,…

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

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Q: 6. Solve y sin (x) cos (x) with initial condition y'(7) = 1 and y(7) = 0.

A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

Q: If e /2i -sin2 then z = - 2 In(sin2) + 4KTO - 2i In(sin2) – 4kT 2i In(sin2) + 4k TO - 2i In(sin2) +…

A: Given e(-z/2i) = sin2 We need to find z. The solution is given below.

Q: The minimum value of cos x + 3 sin x + 5 is: - V10e A 5 - V10- в 5+ V10 D -5 - V10

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Q: Solve: (cos x) · (dy/dx) + y sin x = 2x cos2 x, y(Tt/4) = (-15/2-n2)/32.

A: The given differential equation can be written as :            dydx +ytanx = 2xcosx So, the…

Q: 5. Solve for 0 <e < 2n : 2 sin 0 + V3 = 0

A: Given equation is 2sinθ+3=0 in the interval 0≤θ&lt;2π

Q: 1) If y = (x-a)√2ax-x² + + a is constant. x- -1(*-ª) ,then y' = 2√2ax - x² a² sin-¹ a²

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Q: 1. f/² sin () cos (+) sin (²) d dx (Consider initially the first 2 terms)

A: We have to use the formulas for 2sin(A)cos(B)-sin(A+B)+sin(A-B) and 2sin(A)sin(B)=cos(A-B)-cos(A+B).…

Q: Q4/ Find only five of the following: 1-[t cos at 2-f(6 sin 2t – 5 cos 2t 6. 3+2S 3-[( 3 t5 – 2 t3+ 4…

A:

Q: (11) y" +3y' – 2y = e-2"[(20x + 4) cos 3x + (-32.x + 26) sin 3.x] (12) y" + 9y = sin 3.x + cos 2.x

A: We are entitled to solve only one ques at a time and up to 3 subparts only. Given - y'' + 3y' - 2y =…

Q: V = πT -0.5x Sin 4x 4 +8x-cos2x 2 - X²-4 2²- 19.5x 1.478 -1-082

A: To determine the limit of the following equation.V=π-0.5×sin 4x4+8×-cos…

Q: (x²-cos(2x). c. T(x) = x d. T(x) x2. find Q at x = t/4. = 100e-3x + In(4x), k=470, A= 0.01r and x=…

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Q: /2 2 cos x dx 1+ (sin x)² -n/2

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Q: 9. The position of a moving particle as a function of time is given by: x = (4 - 0.11) sin(0.81)…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: π/2 1-z [²6² x cos ydzdydx = = [Show your solution.]

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Q: Solve 12 cos (t) – 2 cos(t) – 4 = 0 for all solutions 0 < t < 2n. - t =

A: We have to find t

Q: a) _*? (1-x²)Z x+3 b) S- x2+2x+5 c) Find the value of sin(tan-1- sec-d) dx d) S x² Vx2+1 e) S Vx2+2x…

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Q: 2. Find a particular solution (without solving for the coefficients) of y(5) + y(3) = x³ – 3x +7+ x…

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Q: 9. Solve for value of x [0, 2 n ] 2 cos x + V3 = 0 а. b. 2 sin 2 x - 1 = 0

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Q: 5. ) Using the Method of Undetermined Coefficients, give an appropriate guess for y,. y(4) + 9y" =…

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Q: (-1)° x*1 (2k –1)! 2k-1 k=0 a) sin x b) cosx c) sin x- x d) cosx-1 e) e* ||

A: Given,

Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: 5) By using the method of undetermined coefficients, if the term of (r(x) = 3x² cos 5x), the exact…

A:

Q: 4x /² sin () cos (+) sin (²) dx (Consider initially the first 2 terms) 3

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Q: Verify y = 4 cos(2x) + 6 sin(2x) is a solution to y" = -4y.

A:

Q: 2. (a) Show that V3 cos x-sin x COS where 0<x<2r . 2 (b) Using the result in (a), solve the equation…

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Q: 1. Given 0 ≤ 0 < 2t, solve -2 sin2 0 + cos 0 0 1,ㅠ ㅇ 지 ㅇ 警, 풍 ㅇ 쯤,ㅠ, 품 -1.

A: Let's solve trigonometric function.

Q: 3 f(x) = x° – cos(x) %3D х — - Solve this question by the Fixed-point method on the topic of…

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Q: (b) Find the solution for cos(x)- (1+x?) – 2xy = with the conditions 1+x2 y(1) = -1, y(2) = 2 and h…

A:

Q: Зл ,2n) then tg 2 1 If α te( V1- cos“(a – n) + a)+ = 0. 3n – 2a sin(5n + a) 1- sin 2

A: We have to prove the trigonometric equation.

Q: 3. x = 2 cos(3t) – 4 sin(3t) and y = 3 tan(6t) at t = 2

A:

Q: $5. (i) show that: sin 0+sin 20 = tan 0 1+cos 0+cos 20 (ii)Find the general solution of the equation…

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Q: i. Find the domain and range of f(x)=2 cos'(4x– 3)–“ and sketch the graph 4 ii. Find the general…

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

Q: 4. Solve the initial value problem (cosy)y' = sin²x cosx , y(0) = Give the solution implicitly. %3D…

A:

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: Q4) Use separation of variables method to solve: d²u ди ax² + =u where u(0, y) = 0 and ду du(x,0) by…

A:

Q: B sin 5x+ sin 3x 1 sin 5x+-sin 3x+c 6 I 10 fcos 4x cos.x dx = ?

A: Given :∫cosxcos4xdx

Q: 9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact.…

A: To find the  value such that given equation is exact  differential equation.

Q: A mass weighing 32 pounds stretches a spring 2 feet. If the mass is initially released from a point…

A:

Q: Q-4) Find the general solution of the Cauchy-Euler equation x'y"+ xy'+4y = sin(In x)

A: Solve the Cauchy Euler differential equation

Q: 10. Using the method of undetermined coefficients, write the form of the assumed particular solution…

A:

Q: Q-1: Integrate the fraction of functions: 1. f- 14a+1 2. sinx- V(1-x) 2-7x-4x2 dx 3. SE 1-sine dep.…

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Q: (cos 6, sin 0) (0,1f G4) 2x (号) (올) 120 3 3n 60 135 45 5x 150 6 30 (1,0) (-1,0) 0,0 180,t 7x 210, 6.…

A:

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

A:

Q: +4-192 sin(4t) + 160 coe(4e) with y(0)-3 and y (0) 3.

A: Given:    y''+4y'=192 sin4t+160 cos4t      y(0) = 3   , y'(0) = 3

Q: ¹{.(²-1)} = Q4. C-1 (a) cosht - 1 (b) (c) 1 2 (d) 1 - cosh t [cos 2t - 1] [sin 2t - 1]

A: Here, to find the inverse Laplace transform of the function: 1s(s2-1)=1s(s-1)(s+1) Now, using…

Q: 2a S (-1)*-1 NT sin x exp[-(nx/a)²t1] T(x,t) = a

A: The given equation is a heat(diffusion) equation.