Differential Equations Answers

How can harmonic motion be described mathematically? Be sure to link correct mathematical terms to correct physics terms – for example, how are the amplitude, period length, and other mathematical properties of harmonic motion waves related to how an object is moving?

Determine the maximum and minimum of the function f (x) = -x3 + 2x2 – x [0.2].

Define derivatives for the following functions


a.) y= √3x^2+1/3t


b.) y= e^-x sin^2x


c.) y= sin2x / sin^2x

For what value of x is the tangent of the graph of the function f (x) = x4− ax 3−4 parallel to the x axis?

Set the following threshold:

Could you help me find the general solution for these equations, please? Thank you

y'''+ y'' = y + x^5

y(y'') = y' + 8x^3

a particle moves along a path y=2cos3x in such a way that the component of its velocity in the x-direction is 4 units. find its acceleration?

A particle moves along a path y=2cos 3x in such a way that the component of it velocity in x direction is 4 units. find its acceleration

The solution of the initial value problem dy/dx=-x/y, y(4)=3 is

Newtons laws of cooling proposes that the rate of change of temperature is proportional to the temperature difference to the ambient (room) temperature. And can be modelled using the equation: dT/dt = -k (T-Ta)

It can also be written as dT/T-Ta = -k dt

Where:
T = Temperature of material
Ta = Ambient (room) temperature
k = A cooling constant

a) integrate both sides of the equation and show that the temperature difference is given by:

(T-Ta) = CoE^-kt

(Co is a constant for this problem)

B) calculate Co if the initial temperature is 70 degrees C and Ta = 20 degrees C?