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Unformatted text preview: x . 5. Plot a trajectory of your choice in phase-space for the ODE below, where b is a small positive number, for example 1 10 , y + 2 by + (1 + b 2 ) y = 0 . 6. Let L be a linear operator that can be applied to vectors y . The null space of L is the set of all vectors y that satisfy the equation Ly = 0 Prove that the null space of L is closed under vector addition and scalar multiplication, that is, (a) if two vectors y 1 and y 2 are in the null space of L , then their sum is in the null space of L as well, (b) the scalar multiple of an element of the null space of L is an element of the null space of L . 7. Solve the initial value problem d 2 y dt 2 + 2 dy dt + 5 y = ( t-3) , y (0) = 0 , y (0) = 0 ....
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This note was uploaded on 09/29/2010 for the course MATH 108 taught by Professor Trangenstein during the Spring '07 term at Duke.
- Spring '07