y(4)−10y‴+25y″=0, y(0)=3,  y′(0)=8,  y″(0)=25,  y‴(0)=0. y(x)=

Q: Determine the x-intercepts of the function g(x) = 2cos(2x) - 1 on the interval [0, 2]. 01 я 5л 6'6 л…

A:

Q: Find y as a function of a if y(0) = 7, y/(0) = -12, y'(0) = 108. y(x) = y" + 36y' = 0,

A:

Q: Is the function f(2) = -2(xy+x)+i(x² – 2y – y) differentiable? If it is, find it's derivative.

A: Consider the given function.

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 the derivative of the function. Ax) = 6x (9 - 8x)* O (- 12x) (9 - 8x)' (6x- 9) O (-181 )(9- 82)…

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Q: Find yy as a function of xx if y′′′−8y′′−y′+8y=0 y(0)=4,  y′(0)=−6,  y′′(0)=130.

A:

Q: Find Y = Coth 1 (x)

A: Given that y=coth-1x find dydx

Q: Find y as a function of a if y(0) = 5, y(0) = 17, y"(0) = 5, y"(0) = 8. y(x) = y(4) — 6y" + 9y" =…

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Q: 9. (a) Find the domain and codomain of the transformation T, (b) find the standard matrix for the…

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Q: Find y in terms of x. dy dx 12x(3x 2 - 1)3, curve passes through (1, -3) A y= (3x 2.1) 4 B y = (3x 2…

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Q: Find f. f ″(x) = 8x3 + 5,    f(1) = 5,    f ′(1) = 4

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Q: 3. Find the slope of the curve of the function y = at the point P (2,-).

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Q: Find y as a function of tif with y(0)=6, y(0) = 7. Y 400g"-729y=0

A: Given Differential Equation Given y is a function of t

Q: Assume that ƒ′(3) = -1, g′(2) = 5, g(2) = 3, and y = ƒ(g(x)). What is y′ at x = 2?

A: Given:

Q: Find the slope of the graph of the function x2+y2=xy+1/4 at (1/2 , 1/2)

A: Given function is Differentiating both sides with respect to x, we get

Q: Find y as a function of a if y(0) = 7, y'(0) = 10, "(0) = 36, "(0) = 0. y(x) = 0 y(4) 12y" +36y" =…

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Q: Find y as a function of x if y′′′+49y′=0, y(0)=8,  y′(0)=49,  y′′(0)=98.

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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.