The y, of y'"-y=2x²-x -3 by using variation of parameters is: .A y,(x)=Ae*+ Be- .B Yp(x) = x – 1 .C Yp(x)=x² + x +1 .D y,(x)= -2x² + x - 1

Q: Find both first partial derivatives. z = 15XVY 15xVy %3D dz az

A: We need to find partial derivative.

Q: Find both first partial derivatives. 18y2 x az %3D ax dz ду

A: The given function is:z=18y2x

Q: (1) y = x³ lnx (4) y=²+1 (2) y = √sinh √tan.x -,u= u= 3x²-2

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Q: Find the differential dy. y = 6x7 + 3x2

A: Given:y=6x7+3x2

Q: Find for the following equation by Implicit Partial Differentiation; дz x³ + y²z4 + 3xyz = 5

A: Implicit partial differentiation

Q: If f(x, y) = y² cos(x) – a° In(y), find the second partial derivative

A: Partial derivative problem

Q: usk 2: Find the derivative of 4x2 + 6y3 = 50 by filling the blanks. %3D (2 xD(x-)+x 6)(y³4)_=__ dy >…

A: We have, 4x2+6y3=50            ⋯⋯1 We know that, from basic derivative formula ddxkxn=n·kxn-1ddxk=0…

Q: Find the value of 0z/0x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation is xy + z3x – 2yz = 0 and defines z as a function of the two independent…

Q: . Form the differential of the system of circles touching the y-axis at the origin.

A: The solution is given as

Q: If f(x, y, z) 2x5 + 3y5 - 8x2y2z2, what is the partial derivative of f with respect to z?

A: The given function is fx, y, z=2x5+3y5-8x2y2z2.

Q: Find the value of dz at the point (1)1, If the equation 5xy+ z4x -Qy2 =4 %3| defines z as a function…

A: Given 5xy+z4x-2yz=4to determine dzdx  at  (1, 1, 1)

Q: solve the differenhal equa hon by varianon of parameters y" + 3y't 2y 7 te* y (x)

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Q: Find the value of ∂z/∂x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation xy + z3x – 2yz = 0, defines z as a function of two independent variables x and y…

Q: 2+ yety y' : 2у - хеху

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Q: ӘТ ӘР V

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Q: Find the given partial derivative. f(x, y) = 2 sin(6x² – y). fy(0, ) =?

A: First we find the partial derivative with respect to y

Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

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Q: If ø = 4xy, find x and y components of the velocity at (1, 4) and (4, 4). Calculate the discharge…

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Q: Solve for the partial derivative with respect to x, y and z f(x, y, z) = x²y + xy² + 2xyz

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Q: 5xy = 4x²z – 3yz2; yx and y,. -

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Q: The partial derivative fx(-1,0) of ƒ(x, y) = xe³ + x² + 1 is equal to −1. Select one: True False

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Q: Using the method of characteristics, find a solution to the partial derivative equation xux + uy = u…

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Q: Find the requested partial derivative. dz z= (3x +4y) ; (2,5)

A: Option D is the correct option. Use the chain rule to find the partial derivative for z w.r.t x.

Q: Find the indicated partial derivatives. y+ Sz az dy ex

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Q: find dy/dx

A: y=∫sec x21t2+1dt.

Q: If =4xy, find x and y components of the velocity at (1,4)  and (4,4). Calculate the discharge…

A: Given that, ϕx,y=4xy    ...1. Let the points be, x1,y1=1,4 and x2,y2=4,4. Consider the velocity…

Q: Find the partial derivative. z = (2² + 2x – 6y)"

A:

Q: find dy of X sin 2y =YCO52X

A: Given: x sin 2y=y cos 2x To Find: To find dydx.

Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: Find the partial derivative Əz Əx for the function z = 8y²√x.

A:

Q: y² + y²eG)° + 2x²•G° x': 2xye 6) Zaye*

A: The solution is given as

Q: Find all the second partial derivatives forf (x, y) = x³y5 + 2x*y.

A: All the solutions are given below.

Q: 5. Given that 8x2 w(x, y, 2) VIVE Use partial derivatives to find the maximum percentage error in w,…

A: Given, w(x,y,z)=8x2y3 z4Percentage error in x, y and z is 1% , 3% and 4% To find: Maximum percentage…

Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

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Q: Find the partial derivative. = (a² + 4x – 2y)° - dz II

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Q: derivative

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Q: Find the solution of the differential formula in partial derivatives = x³ sent +1; y(x,t);…

A: Integrate twice with respect to t and then put conditions

Q: Solve for the second (a) own partial and (b) cross partial derivative of the function below x² + y²…

A: On solving this we will get

Q: If f(x, y) = y² cos(x) – x³ In(y), find the second partial derivative ду дх

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Q: 5/(A)Evalute ex² dxdy. (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

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Q: Find the partial derivative with respect to x of e^y-2*ln(x)-x^3y^2.

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Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

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Q: Find the approximate root of y = 2x2 + 4x – 6 when x = 0.01 using differentials. -

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Q: Find both first partial derivatives. z = cosh xy2

A: Given: z=cosh xy2 To determine: ∂z∂x& ∂z∂y

Q: Find the partial derivative of u = x^2 + y^2 + z^2 - 4xyz

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Q: Find the partial derivative. 2 = (r² + 5z – 6y)“ az ||

A: The given function is: z=x2+5x-6y4

Q: (b) Form the partial equation by eliminating function f from z = f(x?

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Q: Confirm the approximations by using the linear approximation at x = 0

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Q: Solve for the partial derivative with respect to x, y and z f(x,y,z) = x²y + xy² + 2xyz

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Q: Suppose a particular investor derives utility function - U(x, y) - from owning x units of stocks and…

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