Which of the following is a possible solution to y" +k?y = 0 O y = 2 cos kæ O y = k sinx O y = ekz O y = cos k²x

Q: dw Given, w 2iz- sin iz. Find i dz o-2+cos z -2-cos iz -2+ cos iz 2+cos iz

A: option (c) is Correct

Q: -1x 54cos If cos -1 00, prove that b. a x² 2xy ,2 = sin C. COS a+ ab %3D 2

A: Introduction :

Q: (23) If f(x) = sin zx, find the value of fe (x). 23 sinx %3D 23 e. sin x a. 23 b. cosx . 1 cos TEX…

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Q: x cos 2x e3¤ (e) - Va) [z (P) d [2

A: d/dx(uv) = vdu/dx + udv/dx  d/dx(u/v) =( vdu/dx - udv/dx )/ v^2  d/dx(u+v) = du/dx + dv/dx

Q: 20. Which of the following statements are FALSE? dy 2л -5 I If y = In (7 - 5x), then de 7 - 5x 3e3x…

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Q: if(r, y) = e sin 8y, then fry is given by: 2z O 16 e* sin 8y O – 16 e2* sin 8y O 16 e2 cos 8y O – 16…

A: Solving differential equations . To solve the differential equations.

Q: dw Given, w=2iz – sin iz. Find i dz - -2+cos z -2+cos iz o 2+ cos iz -2-cos iz

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Q: can i get step by step help please

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Q: dy If y = x³ cos π, what is ? O 3r² - sin 7 -3x² sin T O 3x² cos T COS O-³ sin + 3x² cсos π

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Q: Which of the following is the solution of [2x + ycos(xy)]dx +xcos(xy)dy =0 a. x? +cos(xy)=c b. x? -…

A: Given differential equation [2x+ycos(xy)]dx+xcos(xy)dy=0. The objective is to find the solution of…

Q: Which of the following is a possible solution to y" + 16y = 0 O y = tan(4x) y = cos(2æ) O y = sin x+…

A: SOLUTION IS GIVEN BELOW

Q: Which of the following is a possible solution to y" +ky =0 O y = ekz O y = cosk'a O y= k sinI O y =…

A: If roots of the auxiliary equation are imaginary i.e, α±iβ then complete solution is…

Q: Which of the following is a fundamental set of solution of y" – 2y' + 5y = 0. {e' cos 2t, e' sin 2t}…

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Q: er +6 近 。 Oe) sin(2a) Od) cos(2x) T SOƆ 7 5 Ob cos(x²) + 2x (,r)so) (e O ap UIS .2 hip If y =…

A: Topic :- Derivative Correct option = C

Q: Which of the following is a possible solution to y" +k²y = 0 %3D y = ekz O y = 2 cos kx y = cos k² x…

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Q: Q3 Suppose that w = x² + y² + z² x = e" cos 0 ,y= e"sin0 ,z = re® aw аnd ar aw Find дө

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Q: What is the general solution of (r +sin 0 cos 0) dr + r (sin 0 + cos 0) de = 0 ? - rsino rcose = C…

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Q: Qq / show thot ifa is a constont then, u(X,t) = sin lat) cos (x) is a solution to

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Q: Find LT of (i) e(2 cos 5t – 3 sin 5t) 3t (ii) e²ª cos? t (iii) e* sin 2t cos t

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Q: u=x? +y² +=?, x=e" cos 2t, y =e" 2t, ==e = =? ôt e“ (sin? 21 – 2 sin 21 +41 +16r +2) Ob. e“ (cos 21…

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Q: Give the general solution to dy 4x sec (2) +y dx a) sec + 4 In(x) = C 4 b) O sin) - = () - 4 In(x) =…

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Q: Which of the following is true for the BVP y" + 16y = 0, y(0) = 1, y () - = 5 with Yg = c1 cos(4x) +…

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Q: 1) Solve det [i4(îĥ.ở)] where ở li ). and în = COS + sin j. (i = V-1)

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Q: 23. sin r cos? "x dr ².

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Q: sint dt (2. cos t3 Select one: 1 A (2. cos t? B. 4(2• cos tj +C OC2 (2. cos t +C D_ 2(2+ cos tj +C

A: Solve the integration

Q: .2 Q3 Suppose that w = Jx2 + y² + z² e" cos 0, y = e" sin0 , z = re® Find aw and ar aw дө

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Q: V. Determine c, and c, so that y(x) = c, sin 2x + c, cos 2x + 1 will satisfy the conditions y(r/8) =…

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Q: The following statement is correct: cos y . sin x •1 cos y . sin x - dx dy. x3 dydx = [* ' ery exy…

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Q: If f(x, y) = e sin 9y, then fry is given by: O 36 e1 sin 9y O - 36 etz cos 9y O 36 ez cos 9y - 36 e4…

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Q: 3x If f(x, y) = e° sin 9y, then fry is given by: O - 27 e3* cos 9y – 27 e3 sin 9Y O 27 eša cos 9y 3x…

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Q: Which of the following is equivalent to: (e-2'e-t cosh t dt 2 L [cos h t] L [e* cos ht] O A.) B.)…

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Q: Which of the following is a fundamental set of solution of y" – 2y + 5y = 0. {e' cos 2t, e' sin 2t}…

A: The second order linear homogeneous differential equation is given by,…

Q: Which one of the following functions is a particular solution of y" + 2y + y = 25 cos(2t) ? 4…

A: First option is correct.

Q: Given that cos(2t) = 2 cos (t) – 1, it follows that L{cos"(t)} =;( +:). O True O False

A: We need to find Laplace Transform of f(t) = cos2(t) But , cos2t = 2cos2(t) - 1  ⇒ 2cos2(t) = 1 +…

Q: Which of the following is a possible solution of y – 4y = 0 %3D O y =-2 cos(r) Oy = -e-2 O y = e" O…

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Q: dz az If z = xyeX/Y, x = r cos(0), and y = r sin(0), find and ar when r = 2 and 0 = %3D az ar (r, 0)…

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Q: your answer in terms of both x and y. (a) x2 - ry + y? = 5 (b) cos(x + y) = x² 1 (c) -- - = 4

A: Use implicit differentiation to find dy/dx

Q: 1. Then we can write (x + jy)" as R"ene and go back to write the result as R"eine as (R"co s(n0) +…

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Q: What is the general solution of sin 0-2rcos²0) dr + rcos0 (2rsind + 1) de = 0 ? %3D O sin 0 rcos²0…

A: Given differential equation is: sinθ−2rcos2θdr+rcosθ2rsinθ+1dθ=0

Q: 1. Which of the following can be solved by separation of variables? (in principle, anyway...) (a) y'…

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Q: What is the general solution of (x + y) da + tan xdy =0 ? %3D O zsinx + cos a + ysina O zsinx + cos…

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Q: A) Let w = 4x2 +4y² + z?, x = p sin o cos e, y = p sin o sin 0, z = pcos o. Find aw/ap, aw/a6, and…

A: "Since you asked multiple questions we will solve the first question for you. To get any specific…

Q: Which one of the following equals (x + y) dæ dy. T/4 OA p2(cos 0 + sin 0) dr dð Зя/4 - 7#/4 " […

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Q: then If z=e sin 0 = ? О а. 1 O a. 2 Ob. 1 2i +2 OC 2i d. Od. 1 2. +2

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Q: Let y=4 In(cos(e3). Let y=4 In co: = Aeßt sinC (e3t) Then dt cosº (e3t) where A = B = C = D = I| ||…

A: y = 4 ln (cos(e3t))