If the solution of y'' -4y' + 8y = 0  is in the form of y(x) = (e^(ax)) *(c1*cos(bx) + c2*sin(bx))

Q: If f(x) = cos(x) +3z³, what is f'(æ)? O f'(x) = sin(x) +3z³ O f'(x) = sin(x)+ 9x² O f'(x) =…

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Q: If j(x) = e(sin(x)+cos(x))² , then j'(x) = 2 cos(2x)el+sin(2«) COS

A: Given

Q: solve et (l-t)? with y coJ=2 and y'Co)=6

A: We have to solve

Q: f(x) = 3x cos ƒ'(x). -1 (2x + 4) − √√/19 − 3x², find

A: Given: fx=3xcos-12x+4-19-3x2. To Find: f'x.

Q: If y = -cos(2t), then y(5)= ?

A:

Q: find y'. (show all the steps please) cos(xy) = x-y^2

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Q: s¯¹(x + 1) − √√14 − 3x², find ƒ¹(x). If f(x) = 3x cos

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Q: العنوان solve b sin ² (3x) cos² (5x) dx 2 8 tan³x dx >

A: First, we need to identify the type of integral we are dealing with. The first integral is a product…

Q: solve A) y''-2y'=6e^2x-4sin(x)

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Use var of par to find a particular solution yp of ( 1² - ²1 ) y = t t₂ t² (y") + t (y') + t²

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Q: solve it y''+3y'+2y=cos(e

A: The given differential equation is

Q: = 4 and f Find the following. Suppose f 3. -5. Let g(x) = f(x) sin(x) and h(x) = f(x) 3 (a) g 3…

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Q: dy Find if y = 4 sin?(3x) dx

A: Here we have to find the derivative of function y which is given as above. Here I am attaching a…

Q: 2) Find the general solution of the equation 1 y""+y' = (sinx)3

A: The  given equation  is  The auxiliary  equation is  given by…

Q: If h(x) = In 2x+8 4 x 3 sin x find h'(x).

A: Given :- To find :-

Q: Solve the equation [cos (2y) - (3x^2)(y^2)]dx +[cos (2y) - 2x sin 2y - (2x^3)(y)]dy = 0

A: To solve the given differential equation. First we check whether the differential equation is exact…

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.