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Calculus B L88 Separable Differential Equations
Definitions
A differential equation contains one or
more derivatives/differentials
The solution to a differential equation is
the set of all functions that satisfy.
The general solution differs by a constant
The particular solution also satisfies any
initial conditions.
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Separable Differential Equations
These equations are easily separated to solve.
Ex1. Find the general solution to xdx ydy 0.
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Ex3. The slope of the graph of f at any
given point is 3 times the value of the
x-coord of that point. The graph of the
function passes through (2,3). Write the
particular solution of f.
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Special Differential Equations
The rate of change of a quantity is
proportional to the amount of the quantity.
The only function that satisfies this is an
exponential function.