4. What is the form of y, given (D² + 9)y = x + tanx? A. Yp = V,sinx + vzcosx B. Y, = v, sin3x + v½cos3x C. Y, = x(v,sin3x + v½cos3x) D. Y, = x*(v,sin3x + v,cos3x) 5. What is the appropriate second equation to solve number 4? A. v,'sinx + vz'cosx = 0 B. v,'(-3cos3x) + vz'(3sinx) = 0 C. v,'(-cosx) + vz'(sinx) = x + tanx D. v,'(3cos3x) + vz'(-3sin3x) = x + tan x %3D

Q: What is y' of y = sin¹ (cos x)? O A. y' = ATHE sin + 1-cos² 1 O B. y' = 1 OC. y'= sin z 1-cos² z OD.…

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Q: Show that u(x, t) = 4 tan-1 I-ut ev where v is constant, is solution of Uxz – Utt = sin(u)

A: To check the given solution satisfy the given partial differential equation, substitute the solution…

Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

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Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: 2 sin? 11. y = 3x 2x2 12. y = cos°V2x – 1 3. 13. у %3D Vtan(х?)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 The Power rule:…

Q: B\ Suppose that = 4 cos? t , x = v3 sin(2t) and 0 < t < n. S d²y *= - tan(2t) and = -sec (2t). 1 dt2…

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Q: By approximately how much will f(x, y, z) = x cos(rz) – 4x – 3y sin(xz) + y - change if the point…

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Q: 1 If z = 2x2 – 3y with u = x² sin y and v = 2y cos x, determine expressions %3D az dz for and du

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: Suppose tan u = %¾ (sm u>0) and tanuo12/5 Ccasx cO]. Ead he exsee velos OR the followly trgeronetnc…

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Q: tan x dy +y sin x dr = 0, when x = 0, y = | O y (3- cos 21) = 2 O y (cos 2x O y° (2 – cos 2x) = 1…

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Q: 3. If y = (sin 4x)², find y' %3D a.) 4 sin4x cos 4x b.) -4 sin4x cos 4x c.) -8 sin 4x cos 4x d.) 8…

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

Q: The solution of the nonhomogeneous DE y" + y = sec?x is O None of these y = c1cosx + c2sinx +…

A: The given DE is, of the second-order and it is y''+y=sec2x which is non-homogeneous DE. So, first we…

Q: Q1: show that1) d/dz [cosz] = -sin z, 2) 1+tan2 z = sec2 z

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Q: Find dx ar and simplify the result whenever possible *+ sin2x sin' 5x 1. y = 2. y sin5x 3. y sin? 4x…

A: Given  The equation is y=-35cot5x3+cot3x3-3cotx3-x

Q: „In sec²(sin2y)dy can be evaluated by writing it as sec2y A sec²(sin2y) - cos2ydy None © In…

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

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Q: dy iven that x = e" cos 3t, y=e" sin3t, show that tan 3t + dx %3D 4

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Q: dy Find as a function of x when y = sin°(x) %3D O 1) 5cos (x) 2) 5sin (x)cos(x) 3) 5sin (x) 4) 5cos…

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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…

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Q: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

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Q: 8:54 1 3. If y = (5x)sin(3x) , then %3D dy %3D dx Type here to search

A: This question is related to differentiations. Solve in 2nd step.

Q: Suppose that w = a7 · exp(2y) · cos(4z) with z- in (+ 5), x = sin (t+ y = In (t +2), z = t.

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Q: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

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Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z *

A: We have to use derivative definition.

Q: Differentiate: y = In cosh (cos 2) O y' = 6 sin 2z tanh(cos 2z) y' = -6 sin 2a coth(cos 2x) Oy = -6…

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) * 1+tan2 z = sec2 z

A: In both solutions i have used the definition

Q: 10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A.…

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Q: 5. If z = f(x, y), where x = r cos 0 and r sin 0, find z and and hence show that: (). (-(( 2 2 dz dz…

A: To find the partial derivatives of the following function in two variables by chain rule.

Q: Ex: If w cos(uv), u = = xyz, y = π 4(x²+y²)' aw find at point (1, 1, 1). əx

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Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: i. Jsin xcos 2x - sin 2x cos xdx

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Q: The solution of the DE (1+ tan x)y'=-secx coty is O None of these siny + In cosx| = c %3D sinx +…

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Q: (2) Show that y=x sinx is a solution to y"+y= 2 cos x.

A: To Show: y=x sinx is a solution to y''+y=2cosx

Q: ,In sec2(sin2y)dy can be evaluated by writing it as sec2y (A @ In sec2( sin2y) · cos2ydy ®/…

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Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

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Q: 3Tt of cSC X du If u = f(x), then dx cos X . Compute %3D 2 sin x и -

A: Given ,  u = f(x)

Q: Determine the concavity of y = 3 + sin x on [0, 2π]

A: The function y=3+sinx on the interval 0,2π. We have to determine the concavity of this function.

Q: Determine an equation for the sinusoidal function shown. 2. 12 21 Oy = 0.5 cos[0.5(x+ x)] + 1.5 Oy,…

A: The general equation of a sin function is given by; y=A cos(Bx+C)+D Where; A→Amplitude of the…

Q: 9. Evaluate y' of y = e-2*sin3x a. 3e-cos3x- 2y b. 3e-cos3x- 3y c. 3ecos3x - y d. 3e-cos3x +y e. Not…

A: Explanation of the answer is as follows

Q: show that1) d/dz [cosz] = -sin z

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Q: 4. tanx dy + y3 sin? x dx %3D 0, whe х %3D0, у%3D 1 о у?(3- сos 2x) %3D2 о у (сos 2x - 2x) %3D 1 о…

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Q: Q1: show that1) d/dz [cosz] = -sin z, %3D 2) 1+tan2 z = sec2 z

A: solution

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x)…

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Q: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…

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Q: 0.5 COS T - In(4 sin z) dz. J0.1

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Q: Q1\ Differentiate the following 1)2xsin-13x x+1 2)y = In Vx-2 1 3)y = sin-1 2x

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