keyideas3

# keyideas3 - c What must cancel from the expression before...

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Name: __________________________ Key Ideas for Tutorial 3 To be submitted at the start of your tutorial on July 22 or July 27. 1. 1. If y 1 ( x ) and y 2 ( x ) are linearly independent solutions to a 2 nd -order linear homogeneous equation, what can you say about their quotient? 2. Consider the reduction of order method for a 2 nd -order linear homogeneous equation. a. What must you be given (or be able to find out yourself first) in order to use this method? b. What is the first step in this method?
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Unformatted text preview: c. What must cancel from the expression before you can actually reduce the order? 3. If { y 1 , y 2 , y 3 } is a fundamental set of solutions, write the general form of every solution. 4. Write a general solution for each differential equation. a. ( D 2 + 2) 3 ( D – 3) y = 0 b. ( D + 4)( D + 2) 4 y = 0 5. Use Cramer’s Rule to write out the solution to Ax = b where x is a vector with 3 components....
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