Ive [y'[x] - a* y' [x] + b * y[x] == 0, y[x], x] DS 3a Va? 4b x {{y[x] e? 4 b x C[1] + e (a»Va? q C[2]}

Q: Differentiate the function y = In (3x² – 6x + 7). Choose the correct setup below to start differe d…

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Q: Find y as a real-valued function of tif y(5) 9, y'(5) = 9. = y = 49y" 140y + 100y = 0, -

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Q: Express f(z) = x-1-iy (x−1)² + y² in terms of z.

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Q: TI. ExereISC Find the x-value of all points where the functions defined as follows have any relative…

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Q: Find y as a function of x if x*y" + 11xy + 25y = x', y(1) = -4, y(1) = 0. y =

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Q: Find y as a function of x if x²y" +5xy - 12y = x², y(1) = −9, y(1) = 9. y=

A: We have to find as a function of .

Q: Find * 1 y" if y =-(x -3x)

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Q: If f(x.y)= x?+2xy+5y² then дудх

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Q: Evaluate the function when x = 1, 3 and 3 3 1) f(x) = x + 2x - 3

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Q: f(x, y) = 8 – + xy. I y

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Q: f(x) 132. Let h (x) = g(x) Find a. h' (1), b. h' (3) , and с. h' (4).

A: Given

Q: Differentiate the function. r(t) = (3²- + 8)i + r'(t) = (6t)i + ( 132 r'(t) = i + (6t)j r'(t) =…

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Q: _____18) Find y' if y= 6+x √4-x²

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Q: The interval in which the function f(x) = 2x – 12x is decreasing is O a. (-0,0) O b. (-0,-4) O c.…

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Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

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Q: k X L n X L n Y d X + dy=o 2 (x²-xy + y²) dx-xydy =o

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

Q: or f(x) = 2x-7 3x - 2

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Q: For the function z = - 8x³ - 2y² - 2xy, find a z(1,-2), andz(1,-2). dz dz a ax' dy ax

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Q: If f(2) = (3z)²a² z+2/a find and simplify f(/@). %3D

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Q: Find a > 1 to express y = 3(2/9)x in the form y = 3(a−x)

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Q: Differentiate the function y = In (3x2 – 6x + 7).

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Q: Differentiate y = x'arctan 2x 2x A. 1+4x2 - 2x arctan 2x 2x3 В. + 2x arctan 2x 1+4x2 C. 1+4x2 + 2x…

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Q: y = 3√x + 4x 2x2 -31 (1) - 1 (-2) - 4 2 х

A: Given query is to find the derivative.

Q: If f(x) =x* + 3x² – x – 15, then f" (-2) would be A. -48 В. -24 С. 24 D. 48

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Q: Let x + y = 28. Find y"(x) at the point (3, 1). "(3) =

A: The solution of the problem is given in the next steps.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.