ODE review

ODE review - Aquickreview FirstOrderODEs LinearODE...

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A quick review…
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First Order ODE’s y Linear ODE is of the form y Solution can be derived using integrating factor method or variation of parameter method y Separable Equation:
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First Order ODE’s (…cont) y Homogeneous Equation*: y Results in a separable equation *Homogeneous equation can also mean a linear ODE that has zero as its “forcing function” on the right hand side
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First Order ODE’s (…cont) y Bernouilli Equation: y By making the substitution y We can get a linear ODE:
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First Order ODE’s (…cont) y Exact Equation: y Thus we seek a solution est for exactness: y Test for exactness: y Solve for F(x,y): y ow we need to solve for A(y) Now we need to solve for A(y)
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First Order ODE’s (…cont) y Thus, the implicit solution is:
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First Order ODE’s (…cont) y Integrating Factors: y In the case the equation is not exact, we can make it exact by multiplying the equation with an integrating factor σ (x) or σ (y) before solving (same steps as before) y If (M N )/N is a solution in terms of x only ( y x )/ y y If (M y N x )/M is a solution in terms of y only
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Higher Order ODE’s y 2 nd order homogeneous equation with constant coefficients
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This note was uploaded on 12/01/2010 for the course MATH 263 taught by Professor Sidneytrudeau during the Fall '09 term at McGill.

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ODE review - Aquickreview FirstOrderODEs LinearODE...

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