(10) The result of (D - 3D,D, + 2D )sin(x – 2y) is (a) -15cos(x-2y) (b) -15sin(x-2y) (c) -13sin(x-2y) (d) 0 (f) Non of these

Q: (с) 4у" + у %3D 4 sin(3x/2), for 0 <x <л, У (0) %3 0, у(л) — 0

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Q: (а) 8а + 2у + 32 %3D 0 (b) z = sin(x) + cos(y) (1) (c) z = sin 2+x2+y? (d) z = ey II 2. 10 2 0- -5…

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Q: 3.4 Find the residue of f(2) = (1 – 2º) sin(1/2).

A: Find the residue of f(z)=(1-z^6)sin(1/z) We know that residue of f(z) is the coefficient of (1/z) in…

Q: 1. Find the Wronskian for y1 = x, y2 = x² and y3 = x³. 2. Find the Wronskian for y1 = sin 3x , and…

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Q: 3. Iim Sin 5x (-) (+) fcx) fcx) - 0-2 o. 84147 0.2 0.24147 -0.02 0.99833 0.02 0.99833 -D.002 0.…

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Q: 3. The value of A. B. C. D. [xsản xdx (1 - x²) 3/2 + C -sin-¹ x - √1 − x² + ² - (1-x²) ³/² + C sin-¹…

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Q: 2 WWw -21 2T -TT TT -2 -4 -6 s(2) = 3sin(x + )-2 f(x) = 3 sin x + 4 A) f(x) = 3 sin 2x + -2 B) f (x)…

A: Please go through the attached solution.  Thankyou . Best regards.

Q: 5 YR-1 U using residue method. (Hint: U(k) = 1 (z-transform)) %3D 4. Solve

A: Consider the provided question, yk-56yk-1+16yk-2=Uk We need to solve using residue method, Rewriting…

Q: 6x-7 4. S 를 In(4x2 + 1)-2 n(2x + 1)-승Tan-1(2x)| + C (2x+1)(4x2+1)

A: 4 Given integral is ∫6x−72x+14x2+1dx. First of all we will take a partial fraction of 6x−72x+14x2+1,…

Q: cos 20 = 3 sin 0 – 1 (1 – 2sin?0) – 3 sin 0 + 1 = 0 2 sin? 0 + 3 sin 0 – 2 = 0

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Q: 2. Solve for y in terms of x for the following equations: a) In(1- 2y) = x %3D b) In(y- 1) - In 2 =…

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Q: 16. Use Theorem 12 to show that 2n r=0

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Q: -2 a -1 23 1 b-a 2 1 4 T -cos³x sin ²x 1 -2 - e b+ a e 3-b - 1 2 NO - 1 1 -1 O 2 1 013 4 1 خدم برد…

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Q: 3 1. Determine the order and the degree: sin x () - e* () = xy dx². a. Order – 2; Degree – 3 b.…

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Q: 2 8. y' + ²y = -x²y² cos x

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Q: 4) USE THE GAUSS-JORDAN 2 0 -3 0 2 0 -4 1 A= 1 -1 1 - 3 0 2 1 - 4 || REDUCTION METHOD (SINE…

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Q: (a) f(x) = - x x – x² 4 (b) f(x) = 3sin(2x) + cos(6) (c) f(x) = sin(3) – 2³ + 4 %3D

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Q: 2'2 (a) sin-'(0) = V2 -1 (b) sin %3D (c) sin-'( – 1) =

A: we have to find

Q: 1. F (x) = sin x+ 2cos x – 5 %3D 2. G(x) = 3e* – 7log;x – 2 * 3. H (x) = 4sec x + 5tanx 4. Z (x) =…

A: Since there are multiple questions. We will solve only the first three questions. If you want to…

Q: 21.2. Find the residue of f(2) = 1/ Cos z at all its poles.

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Q: 9) S(x.y) = sin (x-3y) Ans. .-2 sin(x-3y)cos(x-3y). S.--6sin(x-3y)cos(x-3y)

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: 1 0 x' = 6 1 -6 |x 4 6 1 X = c1 -4 e + c2e'| cos 61 + c3e' sin 61 6. sin 61 - cos 61 6. -4 e' + c2e…

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Q: 3] y = 12x - 2x+ 5 Degree: Sign of LC: as x→-0, y→. as x 0, y -

A: We have to find the degree and sign of LC and find endpoints.

Q: (x-2) (g-9) 2- 3X+uX- %3D 29-u | Sind general Salantion

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Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

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Q: -(sin³(x) + sin (x³) ) dx A 3sin'x + cos (x³) B 3sin?rcos(x³) + 3xr?cos(x³) © 3sin?x + cos (3x²) D…

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Q: 0 2 1 X' =1 1 -2 X 2 2-1 -cos(1)[C(i+3) +5C,2C, + (3 – 1)C,] + sin()[G(i-1)-5G42G1-1(3-1)0 X(t) =

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Q: Cos z Residue of cos. at z = 0 is %3D 1. 1 -1 3. 2 4. 0 2.

A: The residue of a function: f(z) at z=a is defined as Resz=af(z)=limz→az-af(z).

Q: 4) Exercie S Hst 2x+iy be a complex mumber such thet (-s(37)#0Then Re (tent3z))|c equal to: Sin Bx…

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Q: 1 (27 x sin nxdx 27 bE f(x)sin nxdx -sin nx -1. 1-2n cos 2nn COs nx %3D %3D The requirod f 2)

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Q: d x 2. 1+xVI-(Tanin)

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Q: 2) f(3x + cos(x))[3x +2sin(x)-31dx = A) 3x+2sin(x)- 3+C B)13x+ 2sin(x)- 31 +C C) other

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Q: -Z/3 (A) g(x) =-2cos(3x) (B) g(x)=-2sin(3x) (C) g(x) = -2cos (D) g(x) = -2sin (E) g(x) = 2 sin(3x)

A: As per given by the graph, there is given a graph of g(x). Now, The given graph is lies on the y…

Q: 1-2x²=1+x+x²³ 2²-2²-1+2+ -2(-1) (2n + 1)! x²+1 sin x- ---- cos x=(-1). - (2n)! −2+4- 6! tan 'x-…

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Q: -256 – 256/3i = 2 cos () – 2i sin (E 0.46123174148488i A 2 1.946089741159648 – 27 -256 – 256/3i = 2…

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Q: | (6e"+6x° +4 cos x + 2)dx = %3D 6e + x° + 4 cos x + 2x + c O e – x° + cos x + 2 + c 6 O e + x° 4…

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Q: 12) The solution of 2lnx-In(x+ 2)=In2 is a) 0 b) 1 c) {-1,4) d) 4 e) поп 13) sin( 2 csc"1(2)) = b) -…

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Q: (-1)"zən+1 (2n + 1)! sin = 3! (-1)"-2" (2n)! 21 1+r+ (-1)*+1," I+1) -E n-1 2! Pip- 1)(p – 2)a.. 3!

A: f(x)=f(0)+xf'(0)1!+x2f''(0)2!+x3f'''(0)3!+x4f'''(0)4!+ ⋯ +

Q: 6) Use Linear Property to find ( 1- 3 x4)' A) (1- 3 x4) %3D B) – 4x3 C) - 2 D) - 12 x3 7) Use…

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Q: |-3y{(x)+4y,(x)- y (x)+ 2y,(x)+6x– 3– 4sin(x) = 0 2 y (x)- 3y,(x)– y,(x)– 4x+2+3 sin(x) = 0 %3D

A: Given -3y1'x+4y2'x-y1x+2y2x+6x-3-4sinx=02y1'x-3y2'x-y2x-4x+2+3sinx=0

Q: 5) Evaluate the real integral 27T 1 de (5+ 3 cos 0)(13+5 cos 0) by complex variable methods, i.e.,…

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Q: 8. (D² + 100)y = -300 %3D a. y = C, cos 10x + C2x sin 10x - 3 %3D b. y = C1 cos 10x + C2 sin 10x- 3…

A: Solution: (D2 +100)y =-300 The Auxiliary equation is m2+100 =0 m2 = -100 m= 10i , -10i

Q: Express as a product a. cos 5t + cos 6t b. cos x + 2x

A: We have to express as a product  (a)  Cos 5t + Cos 6t We know that  CosC + CosD =…

Q: The set of solutions of y' = -2e-* – 12 cos(4x) + 2 is given by: а) О 2е + 3 sin(4x) + 2x + C 3 b) О…

A: Note the integration of some functions: ∫eax dx=eaxa+C ∫cos ax dx=sin axa+C ∫xn dx=xn+1n+1 +C ;…

Q: S √16 - x² dx X 4+16x2 A)√16-x2 - 4 In X C) √/16 - x² - sin-1 ] + c - C B)√16-x2+4 In 4+√16-x2 x2…

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Find the general solution of y +9y-4 cos 2r A. y -A cos 3x +B sin 3x +c cos 2r B. y -A cos2xr + B…

A: Given: y''+9y=4cos2x

Q: 2) S(3x + cos(x))[3x + 2sin(x) -312dx = A)13x +2sin(x)- 3 +C B)13x + 2sin(x)-31 +C C) other

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Q: 4.3 Can you show me the steps to solve 19?

A: The given definite integral is,

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: 3. у" — у' — 2у %3D5 sin x y(0) = 1, y'(0) = -1 -

A: