g'(x) = 6x2-10x-30 (x2 +6x)2 4x3+18x+10 g'(x) = (x2+6x)? WWXX WXWX

Q: Suppose that x and y are related by the equation Proportionality 1 dt. Vi + 4t² |Show that d²yldx²…

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Q: Evaluate.cuse C for the Constant of integration). 40 t6x-X dx

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Q: Find integrating factor of the equation (x4+y4)dx-xy3dy=0

A: The given equation can be rewritten as   xy3dydx=x4+y4    ∴y3dydx-y4x=x3     Let y4=t…

Q: Find the exact length of the curve. Y=(1/4)x2-1/2 ln(x), 1 less than or equal to X less than or…

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Q: 1) S dx 9-x2 dx 2) J2y-2 x2Vx2 -2 3) dx 2 V1-x2 |3D

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Q: Thank you :D

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Q: Homogenous (2x²y + y³)dx + (xy?. 2 – 2x³)dy = 0 -

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Q: 3. Find the value(s) of k for which y = e satisfies the equation y+2y' = y" derivative) (note: y" is…

A: k = 1+2, 1-2explanation is given in below step

Q: 3 2x+3 Integrate the following function: y = dx x²+3x-5

A: An integral expressed as the difference between the values of the integral at specified upper and…

Q: solve using non-exact (x+4y3)dy - ydx = 0

A: Solving the non exact differential equation

Q: 1. S (x¹+3x²+1) dx 2. f(x³ + x² + x−¹)dx p³ +p²+p+1 dp 3. p3 √ 2² (√z + √z-1) dz 8x³+27 -dx 2x+3 5.…

A: The objective of the question is evaluate the anti-derivative.

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x³–2x)* 1. у- ; d'y/dx? 2. Y = (5x³ + 2)6…

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Q: 2) y = ex + e¯X, 0 ≤ x ≤ ln 2; x-axis 2

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Q: (1)Find the general solution for (- x) dx – (-y) dy = 0

A: Here, the given differential equation is  (2xy3-x)dx-(3x2y4-y)dy=0

Q: [4] S (x + )´ dx [5] S cos²(2x)dx X. V1+x3 [6] S- dx r-2

A: To evaluate the integration of the following.

Q: 2x+2 dx. 5. x2-2x+1 dy 6. 5. if y = (1+ x²)etan-1x

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Q: 4 + 9x x2 The antiderivative of the function f(x) is

A: Solve the following

Q: یک 2. G(x) = L tanz et et +3 -dt

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Q: Q2// A) Derivative following functions by using chain rule m 1) y = Vu, 2) y = 4u, -Va+1 Vx+1

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Q: 1- for y= sech x is equal to: dx a) sech' x tanh x b) 3sech sech tanh x c)-3sech2x sechx tanhx

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

Q: General solution for xy dx + (2x2 + 3y2 - 20) dy = 0

A: General solution for xy dx + (2x2 + 3y2 - 20) dy = 0

Q: Use variation of parameters to find the general solution: x^2y''+xy'-y = ln (x)

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Q: d’y - 2 y = 5x' + In(x²). dx

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Q: Find the total derivative dy dw. Y=3x+2w+5z x=4 In(w*) z=e43x³

A: Given, y=3x+2w+5z2x=4ln(w2)z=e-z+3x-3

Q: 2. Find y' by implicit differentiation. (5) xy =1+ xy

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Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 2 1. Z= 1+x? ; d²z/dx? 2. Y = (3x + 2)* ;y"…

A: Given function is: y=3x3+24 We have to calculate d2ydx2 or y''. Now we see,…

Q: 3. Find dy/dx y=3^(x^2-1) x ln(3x-5)

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Q: 4 For the function y = 1 e - dy the second order derivative dx? is

A: Given that a function and find second derivative of this function (d2y/dx2). We know that d(xn)/dx =…

Q: dx 15. S (x²+36) ³/2

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Q: Solve the problem by using Exact DE 3 1. (2 x³ x y² - 2y + 3) dx − (x² y + 2 x) dy = 0

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Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: Solve by integrating factors found by inspection: y (x2 - y2 + 1)dx - x (x2 - y2 - 1) dy = 0

A: To solve: y(x2 - y2 + 1)dx - x(x2 - y2 - 1)dy = 0 ⇒yx2 dx- y3 dx+ y dx - x3dy +xy2dy +xdy = 0

Q: Zx+1 8) I = - dx 7-7x+12

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Q: 2 1. Z =- 1+x2 ; d²z/dx?

A: z=21+x2

Q: 4. For the given derivative, find the antiderivative that satisfies the indicated condition. f '(x)…

A: We have to find the anti derivative of the function or we can say that we have to integrate the…

Q: 1,- X73X+2 dx (x+リ) Izafhinx dx Ax. Iォfュース alx dx X43X+2 X+1

A: Since, you have posted multiple, we will solve only first part. If you want solution of other…

Q: What integrating factor should be used to find the solution of the equation ydx + (xy + x- 3y) dy =…

A: Given that: ydx+(xy+x-3y)dy=0

Q: Use integrating factors to solve (x² + y² + x)dx + xydy = 0.

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Q: Please solve this using non-extract 2(x³+xy²+y)dx+(2x²y³+4xy²+ 2x²y+x⁴y+2x)dy=0 ; y(2) = 0

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Q: (メ2メ+Sx )dx h- Cos3x dk 120 x3-XSinx+ CusX dx C. 130 x41 (2メーリdy

A: As per our policy, I can only provide you solution for first three parts, but part (c) is not clear…

Q: 9. S sec 2x dx 10. S cos x esin x dx 11. dx x+1

A: Evaluation of the above integration is

Q: Use Green's function to solve: y"-4y' + 3y e, y(0) = 1, y'(0) 1.

A: Let y1x and y2x be the homogeneous solution of the initial value problem y''+pxy'+qxy=fx, yx0=y0 and…

Q: Vx2tan4x2 dx 2. S (2cos2x2-1)2 dB 3. S 1+e2B 2lnx+1 dx 4. ((Inx)2+Inx) x

A: Given:  2 ∫x2 tan4x2 dx2 cos22x2-123 ∫dβ1+e2β4 ∫2 ln x+1ln x2+ln xdxx  To Find: To evaluate the…

Q: Vaz x² S. (2) dy dx

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Q: What is the value of the differential if f(x) = x + 2x - x = 2 and dx = 0.63. Round your answer to…

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Q: (x-G -0 +2) dx + 2(x+2y+2) dy:

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Q: y

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Q: xydy+(x^2-3y)dy=0

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Q: [2x.ex dx=2x.e-fe.2dx =2x.e- er.2 =2e* (x-1) H.W. 2-1x3.ex de 3- f x2. cosx dx 들 27

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