f (x, y) = x+ 5y 2 +y = 25,

Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

Q: 2x :S dr f(x, y) dy. f (x, y) dy. •1-x² f (x, y) dy. -V1-r

A:

Q: d²y dy – 4 + 4y = e2t.t dt2 dt

A: our objective is to solve the differential equation

Q: (ux – u² – x²) dt max subject to х %3D х + и, х(1) 3 2.

A: As per the question we are given a optimization problem, and we will find the optimal control law by…

Q: - f(x, y) = Vx5 + y5. Find f-(0, 0).

A: Given that fx,y=x5+y55.It is required to find fx0,0.

Q: Evaluate the integrals

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Q: Evalute fi f (y³ – xy)dydx -

A: NOTE: As per our guidelines, I have solved the first problem. If you want the answer of other,…

Q: 2x –1 1 , show that y"+ y' + xy +1 c) If y =-

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Q: f(x, y) = x + y' subject to x + 4y = 29 occurs.

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Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

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Q: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

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Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = 2x3 + 3y2 + 1.

A: To verify that

Q: Find d²y if y =x² +3x-7 and x=2t+1. dt?

A: y=x2+3x-7 and x=2t+1

Q: If f(z) = (t³ + 5t2 + 3), dt then f''(z) =

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Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

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Q: Integrate f(x, y)

A: The region is defined as, Consider the conversion formulae from cartesian to polar coordinates,…

Q: If f(x,y.z)= In(x2 +y³ +2z5), Find and dx² dz2

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Q: d²y dy +2 + 5y = 5t2 dt? dt

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Q: Resuelva yDx - 2(x+y) Dy=0 O x² + 2y = cy² Ox+2=cy² O x + 2y = cy² Ox+2y=c

A: Given differential equation y D x-2(x+y) D y=0 The objective is to solve the differential equation.

Q: Compute (T2 T)(x, y). T(x, y) (3x, 7y), T2(x, y) = (x-y, x + y)

A: We have to find T2 composition T1 .

Q: Find fx, fy, fz f(x,y,z) = x – V2y² +z?

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Q: Integrate f(x, y) = y(x² + y³) 3 over the domain x² + y° 0.

A: Given function is fx,y=yx2+y23 and domain is x2+y2≤4 with y≥0 We have to integrate fx,y=yx2+y23 over…

Q: Find f2, fy, and f.- f(x, Y, z) = (4x² + 6y² + 3z²)¯05 fz = fy = f. =

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Q: x, prove that y¨= 2(y² +1)(3y² +1).

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Q: Find (x, y): R = {(x, y): 0 ≤ y ≤ √√x² +1,0 ≤ x ≤ 1} about the x-axis.

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Q: xyz 9. f(x, y, z) = x² + y2 + z2

A: Givenf(x,y,z)=xyzx2+y2+z2To find Domain of above functions

Q: Calculate fw(-1, 2, 0, –1) where f(x, y, z, w) = xy²z – xw² – e2a²-v²-²+2w²

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Q: ||| V3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8.

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Q: f(x, y) = 6 – V4 - x2 - y2 is

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Q: | f(t) dt 20z 4, then f (t) dt is If 4x²+21

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Q: Find fxy(x,y) if f(x,y) = (x² + y²) 7. fxy(x,y) = ...

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Q: f(x, y, z) = V9 - x² – y2 – z²

A: The given problem is to find the surface for the given function of three variables. Given function…

Q: Find fzyz. f (x, y, z) = x°y°z° + xy° + y°z %3D 6-

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Q: C(x, y, z) = 90 + 6x + 4y + z where x is the cost of 1 pound of one raw material, y is the cost of 1…

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Q: F(x,y, z) = 5x² + 2y² + 4xy + xz

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Q: f(z) = 4z² – 2z + 9 إجابتك = Vx %3D f (z) = 4z² – 2z + 9 إجابتك

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Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

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Q: Find Vy where = (x² + y² + z²) e¯¯ √√√x² + y² + z ²

A: Given :ψ=x2+y2+z2e-x2+y2+z2

Q: а. max f (x, y) %3D 4x + 3ху + у S. t. х+4y— 29 3D 0 х+ 4у — 29 — 0

A:

Q: 1. f (x, y, z) = x° ỹ + 4z°y² – xyz + x² – Vz -

A: Given that: f(x, y, z)=x3y+4z3y2-xyz+x2-z53               NOTE: As per our answering guidelines, we…

Q: Find the critical point of the function f(r, y) = – 4+ 8z + 7z - 5y + 6y

A: Find the critical point (x,y)

Q: 3y - t2 dy = 0; y(1) = 1 + y5 dt' 2y4 O t? = y°(3- 2y2) O t3 = y(4- 3y?) O t? = y(7-6y?) O t2 = y²(6…

A: Solve the initial problem:3y2-t2y5dydt+t2y4=0; and y1=1.

Q: Find f, (X,y) and fy(x,y). Then, find fx(-3,1) and fy(-4, - 2). f(x,y) = - 2xy + 3y + 8

A: Given that: f(x, y)=-2xy+3y3+8

Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

A:

Q: Evaluate B: А: Vye-y° dy 3e-4z2 dz 0, 0,

A: There is a general integral that gets calculated with the help of β function. The integral is…

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.