Math 108 Final Exam

# Math 108 Final Exam - applying variation of parameters 4 5...

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Math 108 Final Exam 10 Questions, each worth 10 points 1. Solving an Exact equation. Solve for constant value b such the equation is exact. Solve the equation for this value of b 2. Draw a phase plot, identify the equilibrium solutions and their stability: f(y) = y(y-1)(y-1) identify roots plot f(y) vs. y plot y vs t determine stability of each equilibrium solution 3. Identify a third degree polynomial providing a solution to the euler’s equation problem Use this third degree polynomial to find particular solutions to the problem by variation of parameters (requires that you adjust the original equation by dividing by t^3 before
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Unformatted text preview: applying variation of parameters. 4. 5. 6. 7. 8. Heat Equation with an extra ‘h * u” term where h is a constant. Separation of variables still works, making this an easy problem. 9. Polar Laplace Equation, defined outside a circle of radius a. Solutions must be real value and 2 pi periodic. Solution requires identifying complex eigenvalues that will satisfy these requirements. Laplace equation has conditions u (a, theta) = f(theta) 10. Non-homogeneous sturm louiville problem. Requires solving one equation with an integrating factor....
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