Show that the given function is a solution to the given Differential Equation. a.) y = −cos x [ln(sec x+tan x)]; y'' + y = tan x b.) y = e^3x cos 2x ; y′′ − 6y′ + 13y = 0

Q: A differential equation is an equation involving an unknown function and its derivatives. Consider…

A: In the question it is asked to calculate (i) The solution for the differential equation…

Q: Find numbers A and B such that y(x) = A· cos(7-x) + B. sin(7x) satisfies the following differential…

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Q: Solve the exact differential equation: (2y sin x cos x – y + 2y?e*y)dx = (x – sin? x – 4xye*y')dy

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Q: 7. What is the value of (X-2)2 for the scores 2,3,5?

A: To find : ∑X-22 for the scores 2, 3, 5

Q: c) y' +y = 2 sin 3x + 4e-4x

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Q: Verify that the function y = x sin(x) + x cos(x) is a solution to the differential equation: y" + y…

A: 1 have verified the differential equation by finding each derivatives

Q: Solve the differential equation. dy y + 1 dx O In |x| – ? () = tan - ex - x + tan-'(x) = C In |x| –…

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Q: Consider the following differential equation to be solved by variation of parameters. y" + y = sec…

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Q: 83. Solve the differential equation x+y=(-x² cos x)y². = x(sin²x+C) A. y 1 C. --=x² y

A: Given

Q: y' – 3y + 2y = cos(e*)

A: Given: y" -3y' +2y= cos(e-x) Solution:

Q: y' + y² = 3y tan x tan? x + 1

A:

Q: consider the differential equation dy/dx=sin(x)/y for which the solution is y=f(x). Let f(0) = 1…

A: Given dydx=sinxy, y0=1. By variables separation,  y dy=sinx dx Integrating on both sides,

Q: y = G, cos 3x – C, sin(-3x)

A: The general solution of a differential equation is y = c1cos(3x) - c2sin(-3x) We need to find the…

Q: For an exact equation, Show that this differential equation cos(x+ y)dx= (3y² +2y+ cos(x+ y))cdy = 0…

A: We  are given the differential equation : cos (x+y)dx+(3y2+2y+cos(x+y))dy=0 On comparing with :…

Q: Obtain in factored form of a linear differential equation with real, constant coefficients that is…

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Q: b) Make the substitution x=et to solve the following differential equation: xy" - 3xy' + 4y = cos…

A: Given that the differential equation is          Let the transformation…

Q: 3. Solve the differential equation given that f'(0) = 1, and f(0) = 6. f"(x) = sin x %3D

A: We have given a second-order linear differential equation f''x = sinx        ...(1). With initial…

Q: a) Solve the following first-order differential equations: ER -y- = 2x, given that when y=0, x=+2

A: The given differential equation is:

Q: Solve the following nonhomogenous differential equation: y'''' + 2y''' + 7y'' + 10y' +10y =…

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Q: The degree of the differential equation (y") +y' – y = x is а. 2 с. 1 h no decree

A: We are asked to find the degree of the differential equation.

Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, %3D {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3,…

A: A function is continuous if and only if inverse image of every open set is open

Q: Obtain the differential equation associated with the given non-derivative equation in x and y. y =…

A: Given that obtain the differential equation associated with the given non-derivative equation in x…

Q: Show that y = 1 - x cot x + A cosec x, where A is a constant, is a general solution of the…

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Q: 4. Find a general solution to the equation y' – 3y = e" sin(2x). -

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Q: dy -y- dx 2x, given that when y=0, x=+2

A: We need to solve the given differential equation with its initial conditions. As the equation is of…

Q: Solve the following differential equation cos>x Y = xV dy = xV1-y dx Select one: O a. y= cos(xtanx +…

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