# MATH128 Lecture Notes - Lecture 1: Switch, Product Rule

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12 Aug 2016

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Math 128 Final Review

Chapter 9

9.1 Ordinary Differential Equations

•Linear

•Initial Value Problem (provide y, y’ or y^2) can ﬁnd particular solution

•Separable ODE:

•Particular solution: separate dy and y to the left and dx and x to the right,

then integrate. Make sure to check initial position when x = 0 don't divided

by zero

•General solution: cant solve for c, don't need to show y=…

•Make sure to check for y=0, if 0=0 then another solution

•Use substitution to make a separable (Feb 3)

•First Order Linear (Not Separable)

•General Form: A(x)y’ + B(x)y = C(x) then manipulate to ->

•Y’ + P(X)Y = Q(X), U(X) = e^integral of P(X)dx

•Then multiply the whole ODE by U(X)

•LHS becomes product rule, so integrate both sides

•Solve for y and C

•Mathematical Modelling

•Mixing Problem

•Different rate in and rate out rate. (dx/dt = rate of salt in - rate of salt

out) = (kg/L * ﬂows in rate)-[(amount of salt x / volume-drains out rate

+ﬂows in rate) * (drains out rate)]

•Same rate in and rate out (separable), x/volume only since drain out

and ﬂow in rates are the same

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