Chapter 1: First Order ODEs

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8 Terms

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General Solution

Solution to differential equation containing arbitrary constants

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Particular Solution

Solution that contains no arbitrary constants. When you specify the arbitrary constants in a general solution

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Initial Value Problem

An ODE together with an initial condition

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Bernoulli Equation

y'+p(x)y = g(x)y^a

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Solution process for Bernoulli Equation

Let u = y^(1-a), differentiate and substitute

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Exact ODE

Equation of the form
M(x,y)dx + N(x,y)dx = 0
is exact if there exists a function u such that
du = Mdx + Ndy

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Criterion for Exactness

dM/dy = dN/dx

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Solution of Exact ODEs

u =