Math 224-01: Differential Equations: Reading Homework 3.6
- Driven Constant Coefficient Linear ODEs : what is accomplished in this section?
- Properties of Polynomial Operators : what is the linearity property? demonstrate this with P(D) = D^{2}+3 and the functions y_{1} = e^{t} and y_{2} = sin(2t). what other properties do these operators have?
- Point : how may the general solution to P(D)[y] = f(t) be written? on what property does this rely?
- Point : how do we find the general solution to P(D)[y] = f(t)?
- Method of Undetermined Coefficients : what is the particular solution to (D^{2} - 2D + 1)[y] = 3e^{-t}? 3e^{t}? y'' - y' - 2y = 4t?
- Point : what guesses might we use for a particular solution for (D^{2} + aD + b)[y] = t^{n}?
- Point : how can we get real-valued solutions to differential equations with cosine or sine driving terms?
- Point : what happens if f(t) isn't a polynomial-exponential or if the polynomial operator has nonconstant coefficients?
Math 224-01: Differential Equations: Reading Homework 3.6
Last Modified: Sun Mar 19 14:57:31 2000
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