Use laplace Trans form to Solve the following Initial-value problem: y" +4y' +3y =Sl4-TI), y 6)=\,y'lo) =-3

Q: 2) vting daplace toansfóöre, Solve x" Zt)+4x'Lt)+3=(4) uing = 10 gint yeren that xco) = -3t Ans: ILt…

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Q: 6. Solve (a) y' = 2ry(1+ 7²)-1 (Hint: Separate.)

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Q: y" - 4y' = 0

A: Given: Ordinary equation is  y''-4y'=0

Q: 58. Find an equation for the tangent line to the graph of y = Vx? + 3x at the point (1, 2).

A: The given function is y=x2+3x. Compute first derivative as follows. dydx=ddxx2+3x=12x2+3x…

Q: 2. Solve for y in terms of x for the following equations: a) In(1- 2y) = x %3D b) In(y- 1) - In 2 =…

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Q: Example 4: Solve iv) y" + y = sin2x.

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Q: Solue the guen equaitions %3D

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Q: 4) = sec(x + y) dy dx 2x-2y+1 5) y' %3D x-y

A: See the detailed solution below.  For others, re-upload the question.

Q: 6. у3 2x – Jx² – 1

A: Given function y=12x-x2-1 we want to derivative of given function with respect to x

Q: Give the equation of the normal line the graph of sin" (x³) + (log3 y) 3 aut le 1)

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Q: 31, 32, 33, and 34 Find y" by implicit differentiation 31. 9a22 9

A: Refer to the question , we have to find the y” by the implicit differentiation as,

Q: Find the first, second, and third derivatives of the func- tion. W (t) = 5t² + 4e*.

A: NOTE: Refresh your page if you can't see any equations. . take the first derivative…

Q: 10) Find the tangent line to the curve 16 1 at the point (4 23).

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Q: 3) y`+y=xe*

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Q: CT/4 (x³ + x* tan x) dx J-7/4

A: Given function

Q: 5b. Find y' when =etet ey

A: The equation is given by y = e2+ex2+ey2…

Q: Q.12) The solution of y" + y' = 0 by using power series method , is! %3! a) y(x) = a, – a,(1-+ b)…

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Q: Consider the initial value problem 1 Y1 -4 2 5 cos(4t) [Y1(-1)] [y2(-1). This initial value problem…

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Q: L"( (sa) (S-1)? 1- Find

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Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

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Q: (2.;v3). 1 Find the equation of the tangent line to x? +y²: = 1 at Use exact values in y = mx + b…

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Q: (:) () -0. -6-1 a) i) If A = 2. and B = 5-2 Calculate:- B'(2A) =

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