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topics2 - Topics For Midterm II 3.1 Homogeneous Equations...

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Topics For Midterm II 3.1 Homogeneous Equations with Constant Coefficients Characteristic Equation to find general solutions, solutions to IVPs. (This works only for linear homogeneous ODEs with constant coefficients, although it can be used as a step in solving linear nonhomogeneous ODEs with constant coefficients.) Equations of the form y 00 = f ( t, y 0 ). (Let u = y 0 to reduce to first order. 3.1.28-3.1.33) Equations with no independent variable. (Let u = y 0 . Use chain rule to transform into the form u ( du/dy ) = f ( y, u ), solve this 1st order equation, integrate to find y . 3.1.34-3.1.43) 3.2 Fundamental Solutions of Linear Homogeneous Equations Existence and uniqueness. (Theorem 3.2.1) Superposition Principle. (A linear combination of solutions to a homogeneous linear ODE is a solution.) Determinant definition of the Wronskian. (Calculate Wronskians, given the Wronskian and a function find the other, etc . . . ). Fundamental solution set.

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