If f(z, y) = e sin 8y, then fzy is given by: O 16 e sin 8y 16 e sin 8y O 16 e cos 8y 27 16 e cos 8y

Q: Consider f(x,y) = cos(x² e³). Then which one of the following is correct O!. fx(x, y) = – 3 y² sin(3…

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Q: Q. If z = f(x, y), where x = u cos 0 – v sin 0 and y = u sin 0 + v cos 0, with 0 a constant, show…

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Q: Find af af and f(x, y) = etry In(6y) af 4yln(6y)e^(4xy) af 1/ye^(4xy)+4xIn(6y)e^4xy dy f(x, y) = cos…

A: In the first part the answer is correct but you have mistakenly not taken bracket for 1/y . You can…

Q: If z= r +y, I= e' cos(s) and y= e' sin(s), then %3D 8z as at (t, s) = (1,0) is O-2e O 4e O 2e? 2e

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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: (a) If y = tan x, prove that y = 2(y2 + 1)(3y2 + 1). (b) Find y' for y cos(sin?x). %3D %3D dy (c) If…

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Q: If u = x? + y? + z?, where x = e2t, y = e2t cos (3t), z = e2t sin (3t), %3D du at t= 0 is dt then

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Q: Obtain the general solution using separation of variables. dz = a(cos 0 dz + z sin 0 d0) %3D

A: Separation of variables.

Q: Solve the D. E. to the I. V. P. sinx(e + 1)x'- cosx 1, y() = 0 O (1 + e') (1 + cos x) = 2 O (1 + e)…

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Q: Solve the D. E. to the I. V. P. sinx(e + 1)x' – cosx = 1, y(0) = 0 COSX O In (1 + cos x) = 1 + e (1…

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Q: Is y c + 2 xe Colution to y" + 2y' +y=0. A Verify y= 4 cos (2x) + 6sin (2x) is a solotion to y "44y

A: We will find actual derivatives and checking by substituting in differential equation that, if it is…

Q: 4. Calculate leme/) at (z,y) = (a, 4). sin(z/g) ey2/2 A ev2/2 B 4

A: Here we have to calculate ∂∂xesin(x/y)=? at (x,y)=(π,4)

Q: If z = sin(xy), then dz is A y cos(xy)dx + x cos(xy) dy y cos(xy) + x cos(xy) dy C y cos(xy)dy + x…

A: z= sin(xy)

Q: 27. w = xy + yz+ zx, x = r cos 0, y = r sin 0, % = r0; %3D dw dw when r = 2,0 = T/2 Ər' d0

A: Given that,  w=xy+yz+zx , x=rcosθ, y=rsinθ and z=rθ. To determine the value of ∂w∂r, when, r=2 and…

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: ().小) of af f(x, y)=sin 1+y, +cos %3D %3D X +1 s215 ||

A: To find The partial derivatives of f(x,y)

Q: 6. If w=xy + yz + zx. x =r cos0, y = r sin0, z= r0, Find dw/dr, dw/dO, when r = 2,0 =x / 2.

A: Answer

Q: dz A. If Z = ey sin (E) + ex ze + y + ex cos (2) then show that x əx dy %3D B. If f = x*cosy +…

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Q: • Given f(x, y) = sin(xy), find fry. || a. fry = -x? sin(xy) b. fry = -y² sin(xy) c. fry = y cos(ry)…

A: Topic = Derivative Correct option  = d

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: dy IS let y = (cos r)m " then de sin z

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Q: 275. J coss O sin 0 do y= E COS O Sin Ø d 0 -dy: = Sin O d0 Sy'ldy) S-y'dy Sy'dy 3. (-dg) %3D + C…

A: you asked to check your solutions are correct or not for 275.and 273.

Q: T/2 T (² cos 2y + 3y° sin z) dz dy . Evaluate -1/2 Jo

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Q: Given f(x, y) = 2e" sin(4y) v (0, then V %3D 2

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: 220. Suppose f(x, y) = x + y, u = ex sin y, x = 1², and y = лt, where x = r cos and y = r sin 0.…

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Q: af ar fe Consider f(1, y, z) = r² + y²z² and I=r sin 0, y =r cos 0, z = Or³. Find and

A: The function fx,y,z=x2+y2z2 and the polar transformation coordinates are x=rsinθ, x=rcosθ and z=θr3.…

Q: * f(t)dt = I cos(7z) is given. I- f(r²) = cos(TI) – TI sin(72) I- f(4) = 1 I- F(4) = %3D | %3D Which…

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Q: Let y=9 In(cos(a). in(co(e*). dy = AeBt sinC (e6t) Then dt cosº (e6t) where A = B = C = D =

A: Given expression y=9lncose6t Differentiate the above expression w.r.t "t" dydt=9ddtlncose6t Recall…

Q: Given f(x,y) = ex cos y, Evaluate fx(2,0) A cos 2 B) sin 2 C) 0 D) e²

A: fx is the partial derivative w.r.t. x

Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) Oe2 0 0 O cos 2 O-sin 2

A: The given function is: fx,y=excosy   As we know that; The common derivative; ddxcosx=-sinx And…

Q: 32. Il sin(x + y) = x,'then dx A 1- cos(x+y) (cos(x +,pv) IB 1+ :aas(x + y) cos(x + v) C cos(x + y)…

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Q: . Let w- e*² <in Cyz)- e Yz cor Cxz) Find - W X

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Q: Given z = 2 cos t +35 and y = 8 sin t %3D %3D dx (i) dt -2*sin(t) %3D dy (ii) 16*sin(t)*cos(t) %3D…

A: Given x=2cost+35 and y=8sin2t

Q: Given f(x,y) = eX cos y, Evaluate fy(2,0) O cos 2 O sin 2

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Q: Q:Ifx= sin 6, y = 0,y = cos pe, prove that (1-x )y,-xy,+p°y = 0, %3D dy where y, dy and y1 d

A: Here given that x=sinθ, y=cospθ Taking derivative of both x &amp; y with respect to θ, we get…

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find fy(5,5,0). Leave your answer correct to two decimal %3D…

A: Partial derivatives

Q: Given f(x.y) = e X cos y, Evaluate fx(2,0) e2 cos 2 O sin 2

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Q: • T/4 cos(0) f |/| f(x, y, z) dV = 9p sin(ø) cos(4) dp d0 dø, find f(x, y, z). E f(x, y, z) =|| ?

A: We have to given ∫∫∫Efx,y,zdV=∫0π2∫0π4∫0cosθ9ρ2sinϕcosϕdρ dθ dϕ Now the function which is to be…

Q: A)lf y = sin¯¹ (3) prove Zyy + z = 0 B)Z = 1+ Ini, find [21.

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Q: Which is equivalent to ſ sin y cos(/2) dy? C/2) dy? a.) S [sin("/2) – sin ("/2)] • dy b.) S sin("/2)…

A: The given integral is: I=∫sinycosy2dy As according to trigonometric formula:…

Q: Solve the D. E. to the I. V. P. sinx(e + 1)x – cosx = 1, y(0) = 0 COSX In (1 + cos x) = 1 + e² O (1…

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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: Given f(x,y) = ex cos y, Evaluate fx(0,2) O e² 00 O cos 2 O-sin 2 M

A: We have to find the derivative

Q: Let w = xy cos(t), y = sin(t), then d at t = T /2 is = 7/2 is dt Select one: O a. -1 Ob. 1 O c. 0

A: w=xy,  x=cost,  y=sint Now,…

Q: E(z, t) = ex cos(@t – kz + Þ1) + ey cos(wt – kz + $2) = €;E× +e,Ey %3D

A: Consider the given equation: Where,

Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) A cos 2 B) e² CO (D) -sin 2

A: This question can be solved using the concept of partial derivatives.

Q: USE HOMOGENEOUS LINEAR HIGHER ORDER DE 4. y(4) + 50y(²) + 625y = 0 ANSWER: 4. y = (C₁ + C₂x) cos 5x…

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Q: 3. m y(t) + k y(t) = Fo cos ot, while o # wo; y(0) = yo, y(0)= 0 [ y(t) = (yo - A) cos oot + A cos…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.