MATH 2Z03 Chapter Notes - Chapter 8: Diagonal Matrix, Identity Matrix, Hyperbolic Function

• School: McMaster University
• Department: Mathematics
• Course: MATH 2Z03
• Professor: David Lozinski

Document Summary

Homogeneous: in short g(x) = 0 means homo; g(x) 0 means no-homo: 2 "" 3 " y y, 2 "" 3 " y y y. + + = is not homogeneous because you can bring the 1 to the other side. 1 0 y and then the equation equals 1, not 0. xy. 2 is not homogeneous because you have 7x is not 0. Homogeneous equation (get into this form): a x y n n a n. No-homo equation: a x y n n a n. Over-determined: more than n different conditions for n-order bvp. Under-determined: less than n different conditions for n-order bvp. For homo equations, your general solution is your complementary solution and the particular solution is what you get when you plug in values and find the constants from the complementary solution. Whenever the right side is 0, your only solution is the complementary solution.