find Df, R1 3 1y = (x4)² + 5 2) y = 5-2x 3) y = - X- 2

Q: (D4 + 3D3 – 6D² – 28D – 24)y = 0 (D3 + 3D2 + 3D + 2)y = 0 -

A: 2) (D3+3D2+3D+2)y=0 The auxiliary equation is…

Q: d = V(22 – a1)° + (42 – Y1)² %3D - - (8, -3) and (-5, 6)

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Q: 3. (D3-2D2+D-2) y=0 4. (4D3+28D²+61D+37) y=0

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Q: F .2 .2 x- +y at A=(2, 3), B=(-2, 2) and C=(3, -4).

A: 1.) div F at A(2,3) = <4,6>2.) div F at B(-2,2) = <-4,4>3.) div F at C(3,-4) =…

Q: 1-r-y C * (r* + y° +:')}dzdydx 14

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Q: 3 1) y=--x-1 2 A) B) C) D)

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Q: I. (a + y?) da dy dz; 2: 2<4-a? - ở, z 20 (x².

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Q: 1. (D² -5D³)y = 4 2. (D³ – 5D* + 7D³ +D² -8D+4)y = 0

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Q: d) 2х3у + e2y — 4х + 5x2. e) y = (2x* + 4)*x %3D

A: We have to find the derivative

Q: YA x = y² – 4y (-3, 3)* x = 2y – y?

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Q: Given a – - 2y² = 9y , what is dy 2 dr dy dz 9+4y dy 3z 4y-9 dy dr 322 9-4y dy dr 9.

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Q: Sx, y) = 2r - 3y²

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Q: 4. (D² – D – 6)y = 0; when x = 0, y = 3, y' = -1 %3D

A: Use this auxiliary equation and complementary function

Q: f(x, y) = 8x3 6x2y3 + 7y4 -

A: Given data:     The given function is: f(x,y)=8x3-6x2y3+7y4.   The expression for the partial…

Q: 2 2X-) dy tf2 るメー。 2. Y+2

A: We have to solve the given differential equation.

Q: Find ƒx (x, y)  and ƒy( x, y) .

A: fx(x,y) is the rate of change in f(x,y) in x-direction. We can find the same by finding the…

Q: f(x, y) = 2y – 6ry - x 2.

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Q: )(x-y) dy: 2ydx, when x 4, y=4

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. If y? = 10x , then dx2 d²y 5x А. 2ху 2y 5ху С. D. 2x 2 B.

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Q: (D³ -3D* +4D³ -8D² +16),y = 0

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Q: Find d² y dx² for x³ + y³ = 2 43

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Q: . Find, from first principles, f(2, -1) for f(x, y) = 2a?y³ + e2y. ,2,,3

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Q: d3y find 3 5) If y = 4x + z %3D dx3

A: Given that: y=4x3+3x2

Q: 10. (D² – 3D) y= 9x² = 9x2

A: 10) Given Information: Given differential equation is D2-3Dy = 9x2

Q: x = u3 + 7 ; y= 6u? – 1 d²y ---> dx2

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Q: 9. (D²+4D+5)y-35ex:y(0) --3, y'(0) - 1

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Q: d²y + 4y = 8x² ,y(0) = -3,y'(0) = 0 dx2

A: We have to solve the differential equation using initial conditions.

Q: dy If x³+y³ = 1, what is -? dx² D OC O 22(23 ys 2x(2 − y) y³ 2x y5

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Q: Maanze; Z こ5x +y Subject to Lラトーメ 5x +3y 575 X20,4? 0

A: Maximize Z=5x+y Subject to, x-y≤75x+3y≤75x≥0, y≥0 The graph is,

Q: f (x, y) = v/2x² + y?

A: I Have provided this answer in step-2.

Q: If 4x5 − 2y5= 25, show that d2y/dx2 = −100x3/y9

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Q: d. xy' – y – 5x* – 3x² + 2x = 0 when x = 1 and y = 2 -

A: first write teh differnetia; equation in standard form and then solve.

Q: 1. (4D5 - 8D4 – 17D3 + 12D² +9D)y = 0 2. (D® – D°)y = 0 3. (D3-D2 - 4D – 2) y = 0

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Q: I-y+z=1 2x + 2= 2

A: The system of equations are : x-y+z=12x+z=23x+y-3z=3 Apply the cramer's rule in the system of…

Q: 1 d. y = Vx6+1 Rewrite y = y'3=

A: (d).   The given function is: y=1x6+1

Q: Evaluate d2y/dx2 at the point (0, -9). x = t3 - 3t y = 3t2 - 9

A: Given: x = t3 - 3t y = 3t2 - 9

Q: If y=3xe , then what is d²y. 3x dx 2

A: Let's find.

Q: d (b) sec2(x³) Vx2+6 d (c) dx \(x3-4)5

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Q: Find d²y dx² d²y dx² in terms of x and y. y5 = x6 6 25 X or|c X

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Q: 3. (D² – 3D + 2) y = 2x³ – 9x² + 6x

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Q: 4. Perpendicular to x - 3y = 2 and passes thru (-3,5)

A: given that a line is perpendicular to the line x-3y=2 and passes through the point (-3,5). we need…

Q: vz 3y 8-x2-y? 1. dzdxdy 0 0 x2+3y2

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you. If…

Q: 3x – y + z = -1, -x+ 3y – z = 7, I – y + 3z = -7.

A: Given: 3x-y+z=-1-x+3y-z=7x-y+3z=-7

Q: 4. (D² +D-1)²y = 0 ,when x= y = 0 , y' = y" = 1, y" = -1

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Q: dy If x + xy - 3y = 3, then at the point (2, 1), A 4. 23 2.

A: Given: x2 + xy - 3y = 3 To find: y' or (dy/dx) at (2,1)

Q: d) 2x + y+z=2 X - y +z=7 2x + 2y +z= 4

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 9. ydx - 4xdy = y'dy; y(4) = 1 Ans: -y²=

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Q: 1 y dy Sza 3 (a²-y²)²

A: