If f(x,y)=xe/2+118x?y, then asf at (1,1) is equal to əx²əy³

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: Ans: (x + y)e+y = C y'+--2

A: Given differential equation is homogeneous differential equation which can be solved by converting…

Q: and the net is decribed by the equation y = V1 – x2 – z2, y 2 0,

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Q: Let f(x, y) = 12x² + 7y² + 3x + 3y+ 6 Find D = frz · fy – fåy-

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Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

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Q: find f given f (z, y) = e + 2ry 4y at (0,3)

A: Topic- partial differential

Q: use the Lagrangian method to solve:   U=(x+3)(y+5) given 30=3x+2y

A: Given the relation 30=3x+2y. We need to minimize the value of U = (x+3)(y+5). Substitute the value…

Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: y" - 6y' + qy 2,

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Q: +] has the general solution u(x, y) = e"[f(x)+g(y)] where f and g g are arbitrary functions

A: ∂2U∂xdy+∂u∂x=0let U(H.Y)=e-yf(x)+g(y)

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: 3. Is y(x) = Cisin2x + C2cos2x, where Ci and C2 are arbitrary constants, a solution of y" + 4y = 0?…

A: Given, y''+4y=0 a second order differential equation. To show that y(x) = C1 sin 2x + C2 cos 2x is a…

Q: In(ax) f(x) has a stationary point at Find a and b. bx 2' 3e,

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Q: Given that y' = 2x2 – y + 3y2, where y = 0.5 at x = 2. Estimate the values of y(2.2) using the…

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Q: The y, of y'"-y=2x2-x -3 by using variation of parameters is: .A Y,(x)= x - 1 .B y,(x)=x² + x +1 .C…

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

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Q: Find the general solution of using the method of variation of parameters. d²y dy 2- - 42+ 2y = xe 2x…

A: Given,2y"-4y'+2y=xe2xComplementary SolutionAuxiliary Equation is 2m2-4m+2=0⇒m2-2m+1=0⇒m-12=0⇒m= 1 ,…

Q: If f (x, y) = Vr³ + y³ In(x² + y²)e*in (zy+y') + x³y+ 10 , then f. (1,0) =

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y+ ++ 4y – x16

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Q: Find general solution of y" – 2y' + y = , By Variation of t2+1' parameter method.

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Q: . Find the general solution of (³ + 2y*)y' = 3ya² in implicit form f(x,y) = c. When y(0) = 1, what…

A: We have given differential equation  x3+2y4y'=3yx2…

Q: 7. Eliminate a and b from the equation y =- In(ar +bx) where a,beR-(0}

A: q-7 eliminate a and b from the equation y=12lnax2+bx  this can be written as 2y=lnax2+bx⇒e2y=ax2+bx…

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

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Q: Using the linear approximation of f (x, y) near (x, y) = (1, 0) tells us that f (0.98, 0.05) is…

A: The linear approximation of a function f(x, y) at (a, b) is L(x, y) = f(a, b) + fx(a, b)(x − a) +…

Q: Show that y %3D Cіx-1 + С2х + Cзlnx + 4x2 is a solution to x3y" + 2х?у" — ху' + у %3D 12х?.

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Q: Find the general solution to the DE using the method of Variation of Parameters 8 y" – 4y = e2x + 1

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Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: ind the particular solution of (9x-2yldx- x(6x- yldy-0 when x-1. y=1 To start let y-vx

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Q: dy + 2xy = f(x), y(0) = 4, where xp Sx, 0sx<< 1 f(x) lo, x 2 1 0 < x< 1 y = x 2 1

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Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y* + + 4y – x16

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Q: 1- , L, v² e*dydx 2- S S マーーー ydxdzdy a>0

A: Explanation of the solution is given below...

Q: x²y"+xy'-y= x 2

A: Given Cauchy-Euler equation is x2y''+xy'-y=x.

Q: By making the change of variables u = 2, v = x, find the general solution of yfyy +fyx + fy = 1.

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Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

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

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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: If y = x(x – 1)* then y' at z = 2 is equal to

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Q: Obtain the general solution valid near the origin: 2y" + 9ху' — З6у %3D 0

A: Power series solution of the differential equation

Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

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Q: which is the best definition of a counterexample

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Q: Find the particular solution of xy' – 2y = -x ; when x y = 5 1,

A: Recall: Consider the first differential equation                           dydx +P(x) y =Q(x)…

Q: 2 Verify that for r > 0, y = r is a solution to yy = x. V3

A: Double differentiate to prove the given

Q: (D³ + 2D² − 5D − 8)y = 0, when x = 0, y = 0, y' = 0, y = 2 - -

A: Given  (D3+2D2-5D-8)y=0 and when x=0, y=0, y'=0, y''=2. The formula for differentiation is…

Q: Find the general solution of the di f ferential equation *+ x .2 d²y + (x² – )y = 0.

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Q: Show that y=x² is asolution to: xy- 3xy'+4y=0, and then use reduction of order to find a second…

A: Linearly independent solutions of the differential equation

Q: The function U(x, y) satisfies the equation a²U_a?U + ax2 ' ay2 = -2, at every point inside the…

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Q: Show that xy – 2 = cxy is a solution of (x² + y2 – x)dx – ydy = 0.

A: Given  x2+y2-xdx-ydy=0 dydx=x2+y2-xy

Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.