(8) If w = 5x2 + 2y2, x -3s +t, and y s - 4t. %3D aw and at aw Find as

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

A: The given equation is: (16x+5y)dx+(3x+y)dy=0⇒(16x+5y)dx=-(3x+y)dy⇒dydx=-16x+5y3x+y⇒dydx=-16+5yx3+yx

Q: a. By differentiating x2 - y2 = 1 implicitly, show that dy/dx = x/y. b. Then show that d2y/dx2 =…

A: The given equation is

Q: dw 2+2 (B) Given w-f(z) 3D to find dx

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Q: (x + y – 2) dx + (x – y + 4) dy = 0 |

A: Given:-(x + y - 2) dx + (x - y + 4) dy = 0To find: Find the family of equations

Q: dy Зу +4 Find the general solution: %3D dx 2y + 3

A: Topic - differential Equationd By separating Variables method

Q: Find dy for the given values of x and ∆x.  y = x3 - 2x2 + 3; x = 1, ∆x = -0.1

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Q: The integrating factor (IF) of the equation: (2x³y + 4x<y + 2xy² + xy* + 2y)dx + (2y³ + 2x²y + 2x)…

A: Solution: Given: 2x3y2+4x2y+2xy2+xy4+2ydy + 2y3+2x2y+2xdy=0⋯⋯⋯⋯⋯⋯eq.1

Q: if 3x - 2e Find dy dk %3D

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Q: 5. Find the dy of the followings: dx (i) y = x²lnx (ii) y = (iii) y = (4x² – 20)(6x +5) (iv) y =…

A: dxndx = n.xn-1. Chain Rule of differentiation : If f(x) and g(x) are two differentiable function…

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

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: (d) y" – 8y' + 20y = 100x² – 169xe". %3D - (e) y" – y' – y = exp(5x). %D | (f) y" – 2y' + 5y = e"…

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Q: -2x 5. y" + 4y'+ 4y= e' In x SAL -2.x V = e (2 In r – 3) + Ans

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Q: Compute ∆y and dy for y = x^2 − 4x when changes from x = 3 to x = 3.5.

A: Topic:- application of derivatives

Q: 2²ye+v°-²dx dy dz 1 -1

A: We have to calculate the integral.

Q: -4x-2 FInd given y =-2 dx Sx+3

A: By using partial differentiation.

Q: Q4 Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) %3D x²+1

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Q: dy 2ty(y - 1) dt 3(1 + P):

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Q: dy 5. S: y(1-Vy)2

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Q: 3. (4r'y-15r-y)dt + (r +3y-1)dy = 0 CS Scanned with CamScarner

A: We can solve this using exact equation of differential equation

Q: If ey 9 dy 3x and y(1) = 2, then the particular solution y(x) is %3D dx

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Q: If f(x)=3x^2 + 2y^2 =16 what is dy/dx?

A: Please see the answer below.

Q: integrate the following ∫(y-2 + 1/2y - 1)dy

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Q: I Solve the fllowing FODF 2y(x+y+2) dx + (y²-x²_ 4x-1)dy = o when x=2,y= 3

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Q: In the given y = ,what is its! 2x2 +3 dy ? x+1 2x2-х-3 a) (x+1)(x+1) dx 6x2+4x+3 b) (x+1)(x+1)…

A: Ans :  To solve this question, we will differentiate the given function y with respect to x using…

Q: (3x - y +6) dx + (6x – 2y - 6) dy = 0 Answer: 7x + 14y + 18 In ( 21x - 7y-12) = C. %3D |

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Q: dy 34. = ty² +3t²y with y(-1) = 2 %3D dt

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Q: 5 To-4x D 5-2x NILS (6z²) dz dy dx

A: solution:-∫052∫010-4x∫05-2x-y26z2dzdydx=∫052∫010-4x∫05-2x-y26z2dzdydx=∫052∫010-4x6z3305-2x-y2dydx=∫0…

Q: = 2-x² and f'(2) dy when x = 1. dx 8. Let y f(1+ Ju), - 3.Find

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Q: Show that dC 1.8x - 1.5 - dx Vx2+0.04 and hence determine the value of x that minimises the cost

A: if for a function f(x) at x=a ,f'(x)=0 then we check for f"(x) if it is positive at x=a , then f(x)…

Q: •1 fl-x r4-x²-y 16. x dz dy dx 0 Jo 3

A: See the attachment

Q: -20x-2) SS f(x.y) dy dx + f(x.y) dy dx= f(x.y) dx dy, then g(6a)+h(a)= if (4)6 0

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Q: dy = 6 3y – x- dx

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Q: + 2e* – 4V¤)dx , where f(0) = 7 -

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Q: Find formulas for dy and Ay if y = 7x – 7. %3D - dy = Ay =

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Q: hich of the following is not variable separable? (А) 2ху dx + (х2 + 1) dy %3D0 A ye' dy - (e-y+…

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Q: Q5. Evaluate ſ^₂ ¹¹ xy dx dy. ry+1 y²

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Q: If feF - dr = Sc(4x + 4y²) dx + (x²y) dy, what is.

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Q: .1 S S, x(x² + y²)²/3dydx

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Q: df Find and dx of dy 2 2 f(x,y) = /3x +4y?

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Q: 12. Find dy for y = sec (3x). %3D

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Q: ,5. For y = 3x° - 9x° + 2x, find dx %3D dx 5

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Q: Find dy for the given values of x and ∆x. ; y = 2x3 - 5x; x = -2, ∆x = 0.1

A: Given y=2x3-5xx=-2∆x=0.1 To find dy

Q: Find formulas for dy and Ay if y = 8x – 4. | dy Ay =

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Q: D ifferentiate. a. y = sin(2x3 – 3) 5-3Vx+x5 b. y = x2

A: Please refer to the image below.

Q: find d^2y/dx^2 implicitly in terms of y and x  2y^3=3x^4

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Q: Find the solution of: dy 2y 3x when x = 1, y = -1 dx 2у + ||

A: A differential equation of first order is said to be homogeneous if it is of the form dydx=Fyx. It…

Q: Find dy for the given values of x and ∆x. ; y = x3 - 2x2 + 3; x = 1, ∆x = -0.1

A: Given fx≡y=x3-2x2+3 x=1 and dx=∆x=-0.1

Q: 2. x3 – y3 = c³, find y" %3D d²x 3. x* = at?, find dt2

A: we need to find d2ydx2 from equation x3-y3=c3

Q: (3x -y - 4) dy t (x+y-4) dx = 0, 2. 14

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Q: -3 -2 ²₁ ² [z³(x + y)³] dz dy dx

A: