rl+cos(@) 3 6. Evaluate: 4r dz dr do 0.

Q: Find impicitly, tf e*(eУ — 1) + sin(2x + 5у) %D In(V7) - - сot(2x) y+2

A: Given function is Differentiating with respect to x by using product rule ,we get

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Q: -3 Evaluate: ²¹²² ²³ y cos(z³) dx dy dz

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Q: d'y 6. if y =, dx² 1-cos4x 1+cos4x du

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Q: 2FI 2FI sım nx dx = cos nx dx = 0, where n integer. 0.-

A:

Q: secx 3 Cos%dyd%

A: The given integral is: I=∫-π3π3∫0sec x 3 cos x dy dx

Q: y = cos(a² – 8) COS dy Find da dy da

A: Given function Use the property of the derivative

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A: First of all, consider the given integral value and integrate.Let nx = a.Calculate dx and the limits…

Q: y" +4y=3te' -3 sint + cos2t based on the method of undetermined coefficients. Do not con…

A:

Q: y" + 2y' = 2 – 5 cos(x), y(0) = 0, y' (0) = 1. %3D

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Q: Given x = 2 cost + 38 and y = 5 sin2t %3D

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Q: Q3) Solve (ysin x + y²) dx – („ - 2xy) dy = 0 + cosx %3D |

A: A differential equation of the form Mdx+Ndy=0 is said t be an exact differential equation if it…

Q: e5x cos e5x dx sin²e5x

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Q: 1. Lif f(x,y,2)=2exp(-5xyz)cos(15z) Find ôxôz

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Q: d²y Given that y = -4x cos 2x +4 sin 2x, find dx² at x = 2

A: Given: y=-4xcos2x+4xsin2x

Q: 2z2 cos 5z dz EVALUATE.

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Q: (D² + D)y = 81r² +14 cos(4x) where y(0) = 0 and y'(0) = 3 %3D

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Q: (tan y+2)dy cos y4-9 tan² y -9tan

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Q: Simplify (if necessary) then 2 Compute: y" +Éy' for a2 y(z) = rar (zx+ cosx')] [6(cosh2x- sinh2x)] d…

A: given yz=∂2∂x∂zz2x+cosx96cosh2x-6sinh2x36cos2πxddx3x2 claim- if necessary simplify then compute the…

Q: y=cos(4x) /cos22x-4sin2x cos2x differentiate?

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Q: Simplify (if necessary) then Compute: y" +y' for [6(cosh2x- sinh2x)] d -3x2 dx a2 y(z) = [; (z²x+…

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Q: dy If y = sin(6x – 4), then dx O a. 4 cos(6x – 4) O b. -4 cos(6x – 4) 6 cos(6x – 4) O d. -6сos(6x -…

A: y= sin(6x-4)

Q: What is if z = x²y+sin(ry²)? %3D dz = 2xy + y? sin(xy') az = x² + 2ay cos(xy) 8z = 2xy + y cos(xy?).…

A: The given function is z=x2y+sinxy2

Q: y у +4у%3D 16t cos 2t

A: We have to solve the differential equation…

Q: dx J5+4 cos2 x CO

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Q: (d) y' + 2 sin 2nx = cosh 3x %3D

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: Q2: Evaluate ſGeascos² (y s) ds. COS

A: Using cos2(bs) = (1/2)*(1+cos(2bs) And integrating using by parts.

Q: and y = 3 cos 2x for 0s

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Q: True or false: V · (cosrŷ + Ve* – y°2) = 0. Explain why. r cos

A: Given that  ∇·excosxy^+ey2-y5z^=0 Now, ∇=∂∂xx^+∂∂yy^+∂∂zz^ So,…

Q: (b) Find, where y= cos ecx- dx -4x+7

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Q: y" – 4y' + 4y Cos 4x -

A: The given differential equation is y''-4y'+4y=cos4x ...................................... (1)

Q: d²y for 15 = cos x Find dx? cos x + a°y?

A: We need to find d2ydx2 for 15=cos x+x3y2. Let us differentiate both sides.                    0=-sin…

Q: sec'x dx + tanx sing dy cory

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Q: Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x +x?

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Q: etany) dy cos?(y)

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Q: 5) [| dydx 6) y cos xy dxdy 00

A: We need to calculate by iterated double integral

Q: x7+3x2. Find dy/dx if: (y)² = sin (cos³(* +3: *)) %3D 2

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Q: cos(4x) dx - Find the Cauchy principle value (showing details): J (+5x2+4)

A: Given integral is, I=∫-∞∞cos4xdxx4+5x2+4 So, the function is, fz=cos4xdxx4+5x2+4 Now, consider the…

Q: (D² – 3D + 2) y = 14 sin 2x – 18 cos 2x

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Q: d (cos² 2x)=-2sin 4.x dx 12 Show that %3D

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Q: Obtain the der a) cos(xy)=2y, find y'

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Q: a) Prave that sinlx t Cos-lx = ½ %3D

A: To prove,   sin-1x+cos-1x=π2

Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

Q: Find y" at (2,4) for cos(x²y + 5) = 16. %3D

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Q: y' – 2y + y = 7e" + 75 sin(2x) %3D

A: Given differential equation is…

Q: cos (x-Inx) dady. at.

A: Here, from the limit of integration, the integral is bounded by x=1e,x=1y,y=1,y=1. Plot the curve as…

Q: y" + 9y = 81x² + 14 cos 4x; when x = 0, y = 0, y' = 3. %3D %3D

A: Use rules of ordinary differential equation

Q: Solve the fo llowing D.- E y + y tan X Cos X %3D

A: