If f(x, y) = 4x²y+7xy°, then the total differential of f at x = 1 and y = 1 is : %3D O df = 15 dx – 18 dy O df = 16 dx + 20 dy O df = 15 dæ + 18 dy O df = 19 dx + 21 dy

Q: Let y = V7 – x. %3D Find the differential dy when a = 4 and dx 0.3 Find the differential dy when x =…

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Q: Assume that x and y are both in a differential functions of t and find the required values of dy/dt…

A: Given y=√x

Q: Let y = (x² + 1)5. Find the differential dy when x = 1 and da = 0.4 %3D Find the differential dy…

A: Given function is y=x2+15. Differentiate y=x2+15 with respect to x dydx=ddxx2+15=5x2+14⋅2x=10xx2+14…

Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : - O df = 32 dx + 4…

A: In total differential take the derivative of each terms, put the given values and simplify.

Q: sa (0, ") : If f(1, y) = 18e* cos z + 5 cot y, then the total differential of f at (0, O df = 18 dr…

A: Total derivative

Q: For a function of two variables, z = f(x, y), the total differential of z is given by: dz = %3D…

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Q: Let y = 5x² + 5x + 3. Find the differential dy when x = 1 and dx = 0.1 %D %3D Find the differential…

A: Topic = Derivative

Q: Find an integrating factor for the DE y(4x – 3y – 3) dx +x(x– 2y – 1)dy=0. (A) x2 B y2 y2 (D

A: To find an integrating factor for the DE  y4x-3y-3dx+xx-2y-1dy=0

Q: find Ly for the given differential operator if (a) y(x) = 2e3x, (b) y(x) = 3lnx, (c) y(x) = 2e3x…

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Q: Find an integrating factor for the DE Y( 4x – 3y – 3) dx +x(x – 2y – 1) dy=0_ A x2 y2 D x2

A: In this question, we need to find the integrating factor of the given differential equation.

Q: dy ,the differential equation xtan x + In y)dx +tan x dy =0 reduces to Using the substitutions 2 =…

A: Substitution in differential equation

Q: What is the differential equation of the orthogonal trajectories of the family of curves X = Cy? А)…

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Q: If f(x, y) = 4x? – 8y, then the total differential of f at a = 1 and y = -2 is : O df = 8 dx – 32 dy…

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Q: Given f(x, y) = 4x²y then the total differential df %3D O 4xy dx + 4x² dy O 8xy dx + 4x² dy None of…

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Q: (a) Find the differential dy of y = e#/5. (b) Evaluate dy for a = 0, dx = .1. (a) dy = dx (b) dy =

A: Solved below

Q: Find the differential dy. (a) y = xV7-x dy (b) y = (1+x) dy

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Q: Transform into Bernoullis' form the differential equation (1 + y) dx - (ry) dy = 0. dy E TY dr dy =…

A: The general form of the Bernoullis' equation is dydx+P(x)y=Q(x)yn

Q: (0. ) : If f(x, y) = 12e cos x + 3 cot y, then the total differential of f at is : J, df = -12 dx 6…

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Q: Given f(x, y) = 11x²y then the total differential df = %3D 11xy dx + 11x² dy 2xy dx + x² dy 22xy dx…

A: The function is given by fx,y = 11x2y To evaluate : The expression of the total differential df

Q: Find the differential dy. (а) у — ху5 xv5 – x dy = (b) y = (1+x)-9 dy

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Q: If f(x, y) = 17e* cos x + 6 cot y, then the total differential of ƒ at ( 0, ÷) i : O df = 17 dx + 12…

A: f(x,y)=17e-xcos x +6 cot y

Q: The total differential of the function: z=x*e3y . .A dz = e 3Y dx +3x“dy. .B dz = 3x"e3Y dx +4x°edy.…

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Q: If f(x, y) = 4x² – 6y², then the total differential of f at x = 1 and y = -2 is : O df = 24 dx + 8…

A: df=dx+dy (see step 2).

Q: 2. Find the differential du of the given functions. (a) y = (12 – x²)3/2 dy = -3r/12 – x² dx (b) y =…

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Q: Find the integral surface passing through the curve T: z= x³, y = 0 of the partial differential…

A: We have given a partial differential equation ,  xy∂z∂x - 2x4∂z∂y-4yz = 4x8yey2 We need to find…

Q: (a) Find the differential dy of y = x² + 2x + 5. (b) Evaluate dy for x = 3, dx = 1/2. (а) dy 3 dx…

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Q: What is the integrating factor of the non-exact DE (4xy+3y² – x)dx + x(x+2y)dy =0 ? 2 (A 2 B x2 1 x2

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Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : df = 32 dx – 4 dy…

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Q: What is the integrating factor of the non-exact DE (4xy+3y² – x)dx+x(x+2 y)dy =0 ? 1 A x2 B x2 2

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Q: If µ(x, y) = x" y" is an integratingfac. of the the DE. . (1 + 3xy)dx + (xyl + x²)dy = 0 Then, the…

A: A differential equation of the form Mdx+Ndy=0 is said to be an exact differential equation if it…

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? А)…

A: Find orthogonal trajectory

Q: Find the differential and evaluate for the given x and d/x of the function, y = 3x2- x+ 6, x = 2, dx…

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Q: If f(r, y) = 3x2 – 8y, then the total differential of f at z = 1 and y=-2 is: %3D O df = 6 dx + 32…

A: we can find the total differential as below using the properties of partial derivative

Q: For a eR , Which of the following is the y(t) solution function of the differential equation system…

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Q: If f(x, y) = 19e CoS I +7 cot y, then the total differential of fat (0.) is: 4 O df= 19 dr + 14 dy…

A: Let the function is f(x, y)=19e-xcos x+7cot y Total differential is defined as df=fx(x, y) dx+fy(x,…

Q: The total differential of the function: z=x*e3y . .A dz = 3x "e3Y dx +4x³e3Ydy. .B dz= 3x"dx +e3ydy.…

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Q: 2. Provide the differential for a* = y*. A. dy = a*-'xda + (a* In a – y* In y)dx B. y*-!dy = a*-'xda…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Given f(x, y) = 8x²y then the total differential df ,2, O 8xy dx + 8x² dy O 16xy dx + 8x² dy O 16x…

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Q: Find the differential dy. (a) y = xv8- x %3D dy %3D (b) y = (1+ x)7 dy

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Q: Which of these differentials is exact? (only one of them is exact) (1 – 2xy)dx + (x² + y²) dy O (22…

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Q: 1. Find the total differential dw. x + y +z 3. w = xyz

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Q: (a) Find the differential dy. V3 + x2 dy = (22+3)() (b) Evaluate dy for the given values of x and…

A: Given query is find the differential of y and its value.

Q: If f(1, y) = 17e cos z+ 9 cot y, then the total differential of f at (0,) is O df = -17 dr + 18 dy O…

A: Given that:-     fx,y=17e-xcosx+9coty  we know that total differential is =     df=fxdx+fydy…

Q: find Ly for the given differential operator if (a) y(x) = 2e3x, (b) y(x) = 3lnx, (c) y(x) = 2e3x…

A: Given: L=D3-D+4 (a) y(x)=2e3x Ly=D3-D+42e3x    =54e3x-6e3x+8e3x    =54e3x+2e3x

Q: +z-y=3e' %3D dt dr dy + 2r+2y= e' dt dt

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Q: The total differential of g(x, y) = e*z²-y is at A(1,4) is %3D Select one: a. dg(A)=(8-1)e^(0) O b.…

A: Consider the following function: gx,y=e4x2-y Differentiate gx,y with respect to x taking y as…

Q: Determine which of the following expressions are exact differentials: (a) df = (y + z)dx + (z + y)dy…

A: (a) If the given expression is exact, then there exists a function f(x,y,z) such that

Q: 12

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Q: If f(x, y) = 2x2 – 9y, then the total differential of f at x = 1 and y = -2 is : O df = 4 dx - 36 dy…

A: Given: fx,y=2x2-9y2 To determine: The total differential of f at x=1 and y=-2.

Q: When u = x and v = V4 - x² we have du = dx and dv dx. Substitute the expressions in 4 - x2 terms of…

A: use the product rule to find the differential coefficient