Midterm 1 Flashcards
1
Q
Is a linear combination of solutions to a non-homogenous diff eq also a solution to the non-homogenous?
A
No. Only for homogenous
2
Q
If the Wronskian = 0 what does it mean?
A
The functions are linearly dependent
3
Q
Linear ODE
A
Function involving x (first order) and it’s derivatives. Can only multiply by functions of t, not exponentials or x…
Linear:
(t^2)x’’ + (t+1)x + 1 = sin(t)
Non-linear:
xx’’ + x + 1 = sin(t)
(D^2 + D + t)x^2 = sin(t)
4
Q
Normal on some interval if
A
- Coefficient functions are continuous
- Leading coefficient function ≠ 0
5
Q
Cramer’s rule
A
det(coef matrix) ≠ 0, system has exactly 1 solution
6
Q
Seperation of variables
A
7
Q
Exponential shift:
A
8
Q
Undetermined coefficients procedure:
A
9
Q
INTEGRATING FACTORS
A
10
Q
Integration by parts
A
11
Q
Linearly independent vs dependent
A
12
Q
General solution to linear ODE
A
x(t) = h(t) + p(t)
