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course Mth 279
4/27 10: Help needed.
Query 13 Differential Equations
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Question: Find the largest interval on which the equation
y '' + y ' + 3 t y = tan(t)
has a solution, with the initial conditions y(pi) = 1 and y ' (pi) = -1.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
??????????????????????????/
I'm having problems folowing the book on how to figure this out, i'm in the right section, and all are homogenius, If I set this = to 0, and let psi(t) be a solution to the equation above,
then let psi(t) = c_1y_1(t) + c_2y_2(t)
and the derivative = that only prime the y's, set that into a matrix to solve for our c1 and c2. which leads to y1 and y2 being a set of solutions according to the theroem 4.3. on page 130.
Get nowhere with that,
So I try to let y = good ol' Ae^rt to get r^2 + r + 3t - tan(t) / Ae^rt = 0
rearange to get Ae^rt(r^2 + r + 3t) = tan(t) where y(pi) = 1 and y'(pi) = -1
which way, if any, is in the correct direction, where do I go from here? The book just covers the absolute bare minimum in examples, and i'm having trouble folowing how to get this chapter under my belt.
Could you give me hints, or a head start in where to go so I can learn this? Thanks
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Query 13 goes with Assignment 15, which is Chapter 4.2.
Given time constraints I suggest taking a good look at 4.1, then skipping to Section 4.4. For now, skip Assignments 15, 16 and 17, and come back and pick them up later if you have time.
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confidence rating #$&*:
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Given Solution:
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Self-critique (if necessary):
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Self-critique rating:
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Question: Find the largest interval on which the equation
t y '' + sin(2 t) / (t^2 - 9) y ' + 2 y = 0
has a solution, with the initial conditions y(1) = 0, y ' (1) = 1.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
confidence rating #$&*:
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Given Solution:
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Self-critique (if necessary):
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Self-critique rating:
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Question: Tell whether each of the following is increasing or decreasing, and whether concave down or concave up, in the vicinity of the initial point:
y '' + y = 2 - sin(t), y(0) = 1, y ' (0) = -1.
y '' + y = - 2 t, y(0) = 1, y ' (0) = -1.
y '' - y = t^2, y(0) = 1, y ' (0) = 1.
y '' - y = - 2 cos(t), y(0) = 1, y ' (0) = 1.
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Your solution:
???? Also If I dont get how to do this by the first problem I may need to have a jump start on this as well, but again depending if the first problem is pretty similar in steps to this. s
confidence rating #$&*:
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Given Solution:
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Self-critique (if necessary):
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Self-critique rating:"
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The number of the query doesn't match the number of the assignment at this point on the Assignments page. Check the text section that goes with each Query, as listed on that page.
See also my note advising you what sections you might want to skip for the moment. Sections 4.2 and 4.3 are fairly theoretical and actually make more sense if you've first done solved some actual equations.
I've also gone ahead and posted a version of this Query which contains solutions.
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