Solve the follo wing in itial Value problem by using laplace trans formi- 9y =0 ; yl0) =0 and y'(0)-22 dx dy 8dy

Q: Show your complete solution Find y'if y = arcsine2x.

A:

Q: Find dy/dx for the equation y^2+xy=1

A: Given:

Q: a)x^2 + y^3 =2xy^2 Give the function for dy /dx.   Give the equation of the tangent line at the…

A: our objective is to find the derivative and tangent line

Q: = vt – 2, d²y t – 2. d²y y = t² – 3' dx2

A: x=t-2y=t2-3

Q: Use implicit differentiation to find dz/dx and dz/dy. yz = 2 In(x + z) az dx az ду

A:

Q: Compute for dy/dx. Suppose y is a function of x. a.) y = 2^(cotx) Arcsec(πx) + cos² (π/7)

A: Given: y=2cotxsec-1πx+cos2π/7

Q: 2.x²y+ 3xy? = 2x + 55

A: We will find the value of dy/dx and the equation of the tangent line at point (5,1) in the following…

Q: If y = arcsin(- 5x + 1), dy dr

A:

Q: y= sinh(2n)-글교 dy/dx gi

A: Derivative of sinx is cosx.

Q: If y = arcsin(4x + 5), dy dx =

A:

Q: 2. Use implicit differentiation to find dy/dx: e"y+ In(arcsin 2y) = 3ª ln y + 5.

A:

Q: If x = t +cos t, y= sin t, find d^2/dx^2

A: Given that      x=t+cost , y=sint  Here we have to find d2y/dx2 .

Q: Find dy Ldx For the following (Jy)' =(In tan x)(x") ( sin x)"

A:

Q: If yx^2 + y^2 = x, then the dy/dx is

A: Using derivatives formula.

Q: What is the slope of the tangent line to the curve 9+yey = 9x + ex at the point (1, 1) for the…

A: 9+yey=9x+ex at the point (1,1)

Q: Find y' if y=Cos (sinx)

A:

Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: y"+y=sec³x

A: The given equation is: y"+y=sec3x

Q: Solve the first order o.d.e dy/dx=(1+y^2)e^x

A:

Q: 6. Determine the equation of the tangent to y = :-xex + ex at x = 0.

A: Explaination of the answer is as follows

Q: Find dy/dx: 1. y=x^2cos^4x I don't understand how to explain and solve

A: The given equation y = x^2cos^4x can be written as,

Q: x' +1 5. -dx x'(x-1)

A: