So, which of the following is the solution functiony(t) ? a) y(t)= sinh2t = e* %3D b) y(t) = sin2t – et | c) y(t) = sinh2t + e! d) y(() sin2t + et e) y(t) =sinh2t + e*

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A: According to guidelines we should have been able to solve only one question at a time

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A:

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A: To find: Solve the given differential equation.

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A:

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A:

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A: The solution of the problem is given in the next step.

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A:

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A: Solve using variable separable method.

Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

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A: Solution below

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A:

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A:

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A: dxndx=nxn-1dexdx=exd dx(a.b)=a.dbdx+b.dadxf(x)=2x2+ex2

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A:

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A:

Q: (1) C) What is y'(x) for a function defined by the equation x sin(ay) = y+ e" as it passes through a…

A:

Q: b) Let f(x) = ¹. Find f'(x), ƒ"(x), ƒ"(x) and ƒ(4) (x). Deduce f(n)(x).

A:

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.