a) Use the d'Alembert solution to solve UTM Pu 1Pu AUTM UTM -00 0, UTM 9 ar u(r,0) = UT = cos r, u(r,0) = e*+1. COs UTM

Q: tan²xdx = sin³ydy when x = 2, y = 3

A:

Q: Example 7: Find the solution of y + 2ý + 4y =x cos 3x The chr. Eq. is r? + 2r + 4 = 0 -bt vb2 - 4ac…

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

Q: y" + y = sec x tan x

A:

Q: O y(1) = c, e*" + C,e For each set of solutions below, match the solutions to the general s Prompts…

A:

Q: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: 30.: Compute the indefinite integral: sin20t dt sin10t sin10t a. b. cos10t +C C. sin10t +C 10 d.…

A:

Q: Compute for a real root of 2 cos x – sin vx = i accurate to 4 significant figures using Fixed-Point…

A: 2cosx3-sinx=14  compute for a real root of equation using fixed point iteration method with an…

Q: z cos(2x)) - cos(2x))+

A: here using sin2x = 2sinxcosx                 cos2x = 2cos^(2) x -1

Q: Solve che DE'sin with Euler 2?

A: For the solution follow the next steps.

Q: Consider the following difference equation: fk k = 0, 1, 2, · . . 1+ fk' fk+1 = with fo is…

A:

Q: The non-homogenous solution of the following equation by using variation of parameter method y" + y…

A:

Q: у У1 Уз Уч У 4 | Уб 6 У 7 У 7 64 If y = cos ax, prove that У 2 5 = 0, where y, Ув 8 = dr ту. dx'…

A:

Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

A:

Q: Plz give correct solution. Suppose T in L(F^2) and dim E(3, T) = 2. Prove that T is invertible.

A: The transformation is :  The aim is to prove that "T" is invertible.

Q: Given, y = (1+ cos 2t)-Find dy dt 8 sin 2t (1+cos 2t) sin 2t 5 (1+cos 2t) -4 sin 2t 5 (1+cos 2t) 8…

A:

Q: Use contour integration to evaluate 2π = 5th I: de 1 + cos²(0)*

A:

Q: Differentiate: y = cos(5 e* ) e11 COS

A: Ans is. option a)

Q: Solve sinx-cos² * = cos² = 1 on the interval 0≤x < 2π. п 4 " бп 4 п 3п 2' 2 0, π Ο 0, π, 2π

A:

Q: 4) Find the following by using the substitution z = tan D S 5 dt sint - cost cos e de ii) sin cos 0…

A: Note : As per our Guidelines , we can solve first one as your all parts are not too small . Please…

Q: Show that: 2 2 4: +2} | sin 2y x=1 y=vx TOX dydx = 2y dydx+ _3 x=2_y=vX

A:

Q: how that: (f)=X*(-f) x(t) is even, then b₁=0, an= To

A:

Q: Find [COR cosh’(t) sinh(t) dt . 2

A: To find the following integral.

Q: Find y for y=tan-(e*+ /x +1) O None of the other answers 1 ex + 2/x y = V1-(e"+Jã+1)* 1 ex + 2/x…

A: I have stated the used formulas in the solution

Q: 5) S V2 + sin 3t · cos 3t dt

A:

Q: First and second derrivative of: y=5 /(sin 3x+cos3x)

A: the given function is: y=5sin3x+cos3x we have to find the first and second derivative of the given…

Q: 48 The complete solution to Au = is -32 :) +-( 7). = What is A?

A:

Q: Queston s Show thak the equation Cos xdoct +?) sin xdy =o is not exact obsain an the equeition in…

A:

Q: Calculate Ehe Value of:(o00001 (0000001A in GF () witlh vmc) =x°+x+X++

A: It is given that

Q: 2014. (₁) flts = filt = Are Length 2 = 0 X7, > 36s1u2+36 cas ² 6 + +9 3√5 dt ₂ 36 +9 = (+²+3) ²…

A: Solution:

Q: LINEAR DIFFERENTIAL OPERATOR N FUNS TIO

A: