Equations with the Dependent Variable Missing For a second-order differential equation of the form y” = f(t, y'), the substitution v = y', v' = y" leads to a first-order equation of the form v' f(t, v). If this equation can be solved for v, dy dt = then y can be obtained by integrating = v. Note that one arbitrary constant is obtained in solving the first-order equation for u, and a second is introduced in the integration for y. Use this substitution to solve the given equation. (1 + t²)y" + 2ty' + 9t−² = 0, y(1) = 6, y′(1) y(t) = ==

Q: (√2-i)-i(1-√√2i)

A: Follow the procedure given below.

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A: To find out the given partial derivative.

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A: Here we have to use the concept of partial derivatives

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A: Vertical asymptotes : It occurs where the denominator of a rational function approaches zero.

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A: NOTE: Refresh your page if you can't see any equations. . the given function is  and we want to…

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A: Here we have to use the concept of derivatives

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A: Assume the given integral be I. I can be integrated via trigonometric substitution by substituting…

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Q: If 2 cos 2t = 1/5 then sin² t = Select one: O True O False 13 30

A: We can find the answer as below.

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Q: Please help me understand and the steps taken in the process. Thank you Given Find the following. a)…

A: Given: fx,y=x3y2-3xyWe need to find a) fxb) fy

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A: use the property of definite integral.

Q: Use integration by parts to find the indefinite integral. (Use C for the constant of integration.…

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A: Concept: Newton raphson method: Another numerical technique to roughly determine a polynomial's root…

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A: Here we use the method of substitution y=vx then dydx=v+xdvdxsee below the calculation and…

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A: use the substitution method for solving the integral.

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Q: 2 +81 1/s(3² +9) ²0 ds

A: The given integral is (s4+81)/[s(s2+9)].

Q: Find the indefinite integral using any method. (Use C for the constant of integration.) 5x + 6x (x²…

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Q: 18 (x² +9) (x+3) -dx

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Q: y-values 86 9* 7- 6 5 4- 3- 2 1 g(x) 1 2 3 x-values If f(x) = g(h(x)), then ƒ' (1) = Submit Question…

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Q: Use MUPAD to determine the following indefinite integrals (7.1) (7.2) (2ax-x²)³ dx. S (7.3) Obtain a…

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A: The average value of fx=x+2 on the interval 1,4

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A: Given: y=arctanx+x1+x2Recall the formulas:ddxarctanx=11+x2     ..........1ddxuv=vdudx-udvdxv2…

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A: We are asked to find the intersection point.

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Q: Let z = √7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2.

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Q: Find the following Wronskian: W(4, 3t, e-³¹, te-³1) O-972e-6t 0-972e6t 6 972e6t O 972e-6t 00 O-6

A: We can find the Wronskian .

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Q: Find f" (x), given f(x) = sec x. O f" (x) = sec³ x tan x Of" (x) = sec a tanz Of" (x) = sec³ x + sec…

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Q: The result of the integral / is equal to 8 (x − 2)(x + 2) - -dx Select one: ○ In |x − 2] − In |x +…

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Q: x+3y=x².

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Q: ve the given init value problem. dy dx 3x²y + y² 2x³ + 3xy' y(2) = -3

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Q: Evaluate: lim 8118 x6x² + x²-1 8x6 + 4x³ + 10

A: see below the calculation and answer

Q: 2. Find the limit algebraically by factoring the expression first. lim x-10

A: