notes 3-1 - t ? EXAMPLE. Solve the initial value problem y...

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SECTION 3.1 SECOND ORDER LINEAR ODE’S WITH CONSTANT COEFFICIENTS The general second order linear ODE can be written in the form P ( t ) y 00 + Q ( t ) y 0 + R ( t ) y = G ( t ) . When G ( t ) = 0 (identically), we say the equation is homogeneous . Turns out that if we can solve homogeneous equations, then we can solve nonhomogeneous ones! We specialize further to the case where P,Q, and R are constant functions. We are lucky because (1) we can always solve the DE, and (2) lots of DE’s in applications are like this! EXAMPLE. Solve y 00 + 8 y 0 + 15 y = 0. EXAMPLE, CONTINUED. Now add the initial conditions y (0) = 3, y 0 (0) = 1. What happens to the solution as
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Unformatted text preview: t ? EXAMPLE. Solve the initial value problem y 00-2 y-3 y = 0, y (0) = , y (0) = 3. Then nd so that the solution approaches 0 as t . What happens if we are just a tiny tiny bit o when we start this system, that is, we start not with y (0) = but with y (0) = + ? Assume we continue to hit the desired y (0) on the nose. What if we get a repeated root? How do we know we have all the solutions? What if the roots are complex numbers? HOMEWORK: SECTION 3.1...
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This note was uploaded on 05/19/2010 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas at Austin.

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notes 3-1 - t ? EXAMPLE. Solve the initial value problem y...

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