Suppose a solution to a differential equation is given by: x(t)=5cos(2t)+12sin(2t) (a) Express the function x(1) in terms of x(t) = Acos(2t +) or x(t)= Asin(2t +ø). (b) What is the period and amplitude of this motion?

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A: The solution is given as

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A: From the given information. The given differential equation is as follows.

Q: Find the derivative of 5e* 1. y = e 6x 3. y = 2x+3x 2. y = e* + e3x 4. y = (e* + ex)1/2

A: Quotient Rule of differentiation : ddxuv=v.dudx-dvdx.uv2 deaxdx=aeax dxndx=n.xn-1

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.