For the given differential equation, apply the Laplace transform and solve for Y(s) = L{y}- %3D y" + y' – y = 0. y(0) = – 1, y'(0) = 2 %3D Y(s) = e^(-12)cosh((sqrt(5)t)/2}+3] * Preview

Q: (c) Find the differential of the function: l =e"sin(s+ 21 )

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: y = V In(5x + 7)

A: In this question, we use the chain rule to find the derivative of the function .

Q: y" - 2y' = -4 y(0) = 0, y'(0) = 4

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Q: solve the differential equation using integrating factor. ((y(e^xy))+sin(x)) + (dy/dx)(e^xy)x = 0

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Q: CALCULATE USING A HOMOGENOUS EQUATION. GIVE THE GENERAL AND PARTICULAR SOLUTION. SOLVE NUMBER 3 THE…

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Q: y" - y' - 2y = 5 sin x y(0) = 1, y'(0) = −1

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Q: Find y'. In(5x) y = 4x y' =

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Q: Find the derivative of f(x) = log, (x° + x – 1). %3D 2 + x - 1 f (2) = %3D (3z* + 1) (In 2) (3z +1)…

A: Given:     fx=log2x3+x-1

Q: Solve the IVP y"(1) +y'(t)- 2y(1)= 2e' sin(t), y(0) = 1, y'(0) = 1. %3D

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Q: y" - y = 4 cost y (0) = 0 y'(0) = 1

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Q: 0 6 417 8x dx ㅋㅋ 0 3,417 an ○ 2x-417dx 34/7) ㅊㅈ -417dx ○ 2x1017 dx

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Q: Find y'. y = V In(7x + 5) y' =

A: Given the function y=ln(7x+5)         ........(1)

Q: Use implicit differentiation to find y' for 4x³y² + ln(xy³) Answer exactly. y' (1, 1) = 4 and then…

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Q: Find the derivative of the following: y = (2x + 3) (3 – a²)

A: Given, y=(2x+3)(3-x2) To evaluate derivative of y

Q: Find y'' in y = (1 + 1/x)3

A: We first expand the given expression first.

Q: Calculate the increment and differential of the function y=x+2/x+1 at the point x=0 when Δx=0,1.

A: The increment of the function: y=f(x) is calculated using the formula: ∆y=fx+∆x-f(x). The…

Q: Find the solution for this second ODE y(0) = 1, y'(0) = 1

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Q: Differentiate h(y) = ln (3y) sin y

A: To differentiate the function  h(y)= ln(3y)sin-1y

Q: Solve the bernoulli equation dx/dy+(2/x)y=-x^2y^2cos(x)

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Q: Calculate the first, second, and third derivatives of y(t) = 2016/5 – 6127. (Use symbolic notation…

A: We will use simple differentiation rules to solve this question.

Q: Cx²e*dx

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Q: y'' - 15y' + 60y = e^x cos(16x

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Q: Find y'. In(5x) y = 7x

A: SOME RESULTS:     IF y= f(u) and u=g(x) then,  dydx=dydududx.      ddxuv=vdudx-udvdxv2,v is non…

Q: ou are given the following differential equation:  (1/x4)(dy/dx) + (1/x2)y = x5, x > 0.  What…

A: Given differential equation A differential equation of the form is a linear differential equation…

Q: y' = x 2 (1+x²)² cos² y solve differential

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Q: Find the derivative of the function. - c() (수 1 - e9x 1 + e9x y = cos y' = 18e9z sin + e&= )…

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Q: y'' - 6y' + 6y = e^x cos(2x)

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