uation Classify each differential equation in terms of partial, first or second

Question

uation Classify each differential equation in terms of partial, first or second or third order, lin separable, and/or autonomous 1. Consider the following equations, all discussed in are the same types of differential equations, can be so same method and have the same graphical solution in terms of ordinary or or third order, linear or nonlinear, sed in Lecture Notes Notes. lved by the dT =k(Z-T), Newton's Law of Cooling dt dC =r_kC, first order kinematics of drug conc dt dl VR dt L L do r.1o, series RC cin 1 , series RL circuit, constant voltage = Q, series RC circuit, constant voltage dt R RC dv dt =g--v, velocity of falling body, with air resistance a. What is the classifications of these equations (all the same) b. What methods of solution can be used to solve them.

Explanation / Answer

a)

Applications of First-order Differential Equations to Real World Systems:The real world problems can be represented by first-order differential equations.

newtons law of cooling,

first order kinetic drug concentration,

series RL circuit constant voltage,

series RC circuit constant voltage,

velocity of falling body

other examples

Cooling/Warming Law

Population Growth and Decay

Radio-Active Decay and Carbon Dating

Mixture of Two Salt Solutions

Series Circuits

First order differential equations. General form: F(y 0 , y, x) = 0 When possible, solve the equation for y0 to obtain the form y0 = f(x, y)

                         

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