51. f(x, y, z) = z In(x²y cos z) (:) XZ f(x, y, z) = y-3/2 sec y 52. 1 53. f(x, y, z) = tan¬1 xy²z3 54. f(x, y, z) = cosh(z) sinh? (x²ya %3D In Exercises 55. C0

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Q: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

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Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sinh (xy - z2)

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Q: Let 2x2+ 3x+Y a) Find the differential dy when x = 1 and dx=0.1 %3D b) Find the difiea ial dy when…

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Q: 16 tan- dx 1 + x? dv 19. 20. (1 + v²)(1 + tan¬1 v) Oe® do 2e-0 sin 0 do 21. 22. e tal dx 2хe dx 23.…

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Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

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Q: 6. Let z = 5e** sin y . Compute the differential dz. A) dz = 20et* sin y dx + 20e** cos y dy B) dz =…

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Q: Find the solution. (y - x+ xy cotx) dx + x dy = 0 xy cosy = c+ sinx - x secx B) x siny = cx+ sinx -…

A: The given differential equation is y-x+xy cot xdx +xdy=0. The integrating factor of the linear…

Q: 10. Find the most general antiderivative; verify your answer by differentiation. 5-4x 2x" b) f(x)…

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Q: Compute Y (II) withe y" y'= -8 (Sinx+cosx. Y(T) = 0, y¹ (F) --8, by @ Taylor Series

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Q: Consider the following differential equation. (sin(y) – y sin(x)) dx + (cos(x) + x cos(y) – y) dy =…

A: A first order partial differential of the form  Mdx+Ndy=0 is exact if My=Nx.

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Q: Find the differential dy of the given function. y = x cos 2x dy Submit Anguer X

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Q: Find the differential of the function. y = V 4 + cos(0) -2 sin (0) dy V 4+ cos (0)

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Q: 2. y' = y sec x ; 3. у(3x3 — х + у)dx + x?(1 — х?)dy %3D 0 4. у(2х — у + 1)dx + x(3x — 4у + 3)dy — 0…

A: 2) y'=y secx this can be written as dydx=y secx⇒dyy=secx dx integrate the function ∫dyy=∫secx dx…

Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

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Q: A copper rod 1 cm long with insulated lateral surface has initial temperature function, f(x) = 2x'…

A: We are given the following PDE:                   ut(x, t)=5uxx(x, t), 0&lt;x&lt;1, t&gt;0Initial…

Q: the initial value DE y' - ytanx = sinx, y(0) = 1 cos 2x 5-cos 2x %3D 4 sin x 5-cos 3x 5-cos 2x В) у…

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Q: Find fyxyx for f(x, y) = ln(xy) − cos (xy) at (1, π)

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Q: 2. Integrate: a) Sx cos(x²) dx g) [3 cos(2nx) dx b) S tan³ x sec²x dx h) Se2% sin(e²*) dx c) S cot x…

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Q: 6. Find S(3y – y³) (1– y?)dy sin ycos y 7. Integrate: J sin² y dy 8. Find 3 S(5 - 3y-5)²dy

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Q: What is the solution of given initial value problem? y+sin t dt d'y dz +cos t (0) = 1, z'(0)-0,…

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Q: Verify the function z(x,y)=Vx sin is a solution of the following partial differential equation…

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Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…

A: The differential equation  d2ydt2+ptdydt+qty =rt                    .......1 with conditions yt0=y0,…