oxymoron
06-12-04, 04:32 AM
I have been doing my calculus revision for my final next week and I am getting stuck on a specific type of question. Here is an example:
Q1)
(300-2t)dM/dt + 4M = 5ln(1000+t), M(0) = 0
An extension of the Existence and Uniqueness Theorem guarantees that the largest interval on which a unique solution exists and is continuous is:
(a) -∞ < t < ∞
(b) 0 < t < ∞
(c) -1000 < t < 150
(d) -1000 < t < ∞
(e) -∞ < t < 150
Q2)
For which initial value problem does the Fundamental Existence and Uniqueness Theorem NOT guarantee the existence of a unique solution?
(a) y' = xy^1/2 , y(0) = 1
(b) y' = xy^1/2 , y(1) = 0
(c) y' = yx^1/2 , y(0) = 1
(d) y' = yx^1/2 , y(1) = 0
(e) All of the above
For those interested the answers are C and B respectively.
The question is... could some give me a quick tutorial on the idea of solving these types of problems, or perhaps a personal account on how they solve them or even hints or their own way of looking at them.
Q1)
(300-2t)dM/dt + 4M = 5ln(1000+t), M(0) = 0
An extension of the Existence and Uniqueness Theorem guarantees that the largest interval on which a unique solution exists and is continuous is:
(a) -∞ < t < ∞
(b) 0 < t < ∞
(c) -1000 < t < 150
(d) -1000 < t < ∞
(e) -∞ < t < 150
Q2)
For which initial value problem does the Fundamental Existence and Uniqueness Theorem NOT guarantee the existence of a unique solution?
(a) y' = xy^1/2 , y(0) = 1
(b) y' = xy^1/2 , y(1) = 0
(c) y' = yx^1/2 , y(0) = 1
(d) y' = yx^1/2 , y(1) = 0
(e) All of the above
For those interested the answers are C and B respectively.
The question is... could some give me a quick tutorial on the idea of solving these types of problems, or perhaps a personal account on how they solve them or even hints or their own way of looking at them.