MATH 255 Lecture Notes - Lecture 10: Linear Independence, Nostril
Document Summary
Systems of odes (i) section 3. 1: in this section, we have learned that every high-order odes can be reduced to a system of rst-order equations, by introducing more variables to represent the derivatives of the solution y(t). , (1) can be recast into u v. = p(x)v q(x)u r(x)y + f (x): This is a system of three rst-order odes. If p(x); q(x); r(x) are constant functions, then there is a systematic way to solve equation (2), as given in sections 3. 4, 3. 7. On the other hand, every system of rst-order odes can be written into a higher-order equation. For example, in exercise 3. 1. 3, the system is. Di erentiate the rst equation with respect to t, we obtain. = 3(3x1 x2 + et) x1 + et. We can then use the method (undetermined coe cients, variation of parameter) we learned in chapter 2 to solve for x1 in the 2nd-order equation.
