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LETU
MATH 2013 -
Intro to Differential Equations
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Intro to Differential EquationsDefinitionVerificationUsing Direction FieldsSeparable Differential EquationIntro to Differential EquationsLesson 5.6Definition•Any equation that contains A derivativeA differential•A solution of a differential equationA function that satisfies the equation•Example: y = x2 is a solution of 3 24 2 7dyx xdx= + -7 cosdy x dx=2dyxdx=Verification•Given•Show it is a solution of this differential equation•Use implicit differentiation to demonstrate the proscribed relationship 2 25 2 3x y- =52dy xdx y=Using Direction Fields•Consider the direction field or the differential equation•Sketch the solution which passes through (0, 0)x ydyedx+=Separable Differential
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