9.1 differential equations
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Transcript of 9.1 differential equations
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First Order, Separable
Differential Equations
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Differential Equation mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders.
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Let’s see some examples !
Solve the differential equation
and then solve the initial - value problem y (0) = 1
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Practice Time!!!Solve the initial – value problem:
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Slope FieldsFinding the solution given a differential
equation is often difficult.We can come up with a visual pattern for
the general solution graphically using slope fields.• Let’s take the differential equation
• Create a table showing several x, y, and y’ values:
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x -2 -2 -1 -1 0 0 1 1 2 2
y -1 1 -1 1 -1 1 -1 1 -1 1
y’ -5 -5 -3 -3 -1 -1 1 1 3 3
Draw short segments represent y’ at the selected points.
We would need more points to give an accurate visual
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