1) Consider the DE: xy' +(5x-1)y = 0. A) Determine whether the DE is linear or nonlinear and find its normal form. B) Find the value of m such that y Tema is a solution of the given DE. =

Q: c) Find i. y' for x4 + y = 17 If x = 3 and y = 3, calculate y'

A: Here is the solution of above problem.

Q: d) Solve: y"+y"-5y' + 3y = 0

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Q: Undefined Slope 17,9), 17,2) X, - X m= 2-9 18 - 16 m%3D y - y = m (x-x)

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Q: Let y = Arcsec (cos² 3x). If y '= == A (B C) D) - 6 tan3x - 3 sin3x - 6 sin3x cos3x N 2 cos3x D and…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: By Lagrange's formula, prove that y =y3-0-3(ys-y- 3) + 0-2 (y_ 3 -y_5).

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Q: Is the given statement true or false? Justify your answer.   'The equation y'=x+y  is separable.'

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Q: Find the general solution af the equation, y' = x(1- y).

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Q: Suppose A is changed to A' .How large a relative change can this change produce in the solution to…

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Q: Suppose that a particle moves according to the law of motion st² 12t+24, (A) Find the velocity at…

A: Since multiple subparts are asked, I am answering the first 3 subparts.

Q: 11. (b) x²y' – 2xy = 3x with y(1) = 3

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Q: Select all the functions that are a solution of y" - y = 0

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Q: Solve the following first order equations: (e" + y)dx + (2+x + ye")dy = 0, y(0) = 1.

A: First order linear differential equation

Q: Verify that the function y = c1e (-k+2t)x + c2e (-k-2t)x is a solution to y " + 2ky'+ (k 2 + 4)y =…

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Q: Find an equation of the form y- ab" I esin(, that fit: the data below 1 2 5 22 80 318 3 To fit the…

A: Given, The equation  y = abx+csinπ2x   and the data  x 0 1 2 3 y 5 22 80 318 We have to find…

Q: Consider the equation x² + y³ + zª − 8xyz = z². Find z point (1,1,1). at the

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Q: The function y1=ln x is a solution of xy''+y'=0 A) Find a second solution y2 on the interval…

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Q: 2. Show that cos(wt – B), coswt, sinwt are linearly dependent functions of t. Show Complete Solution

A: Given that: cos(wt-B), coswt, sinwt

Q: Is the equation t²y' (1) t + 4 - separable? y?

A: t2y't=t+4y2

Q: dy 05: A/ Find the separable equation dx

A: The given differential equation is: dydx= y2 - 1x ⇒ dyy2 - 1 = dxx Solve this equation as follow:

Q: B- Solve the D.E.: y--e* = 0, y(1)=1 .

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Q: Find m such that the function y= Aex satisfies the equation 2y"=y'+y

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Q: (2xy³ + 1) dx + (3x³y² - +) dy=0 y(5)=n Determine the interval ON which the solution exists.

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Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0