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course MTH 279

Query 13 Differential Equations*********************************************

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.

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Your solution:

p(t) = 1, continuous for all real t values, (-∞,∞);

q(t) = 3t, continuous for all real t values, (-∞,∞);

g(t) = tan(t), continuous between (nπ)/2 and ((n+2)π)/2, for n = odd integer values;

The initial conditions are imposed at t = π, so the largest interval is π/2 and 3π/2.

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary): OK

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Self-critique rating: OK

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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.

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Your solution:

y’’ + sin(2t)/(9(t^2-9)) y’ + 2y/t = 0

p(t) = sin(2t)/(9(t^2-9)), continuous for all t ≠ 0,±3 (-∞,-3)(-3,0)(0,3)(3,∞);

q(t) = 2/t, continuous for all t≠0 (-∞,0)(0,∞);

g(t) = 0, continuous for all real values of t (-∞,∞);

Initial conditions are imposed at t = 1, so the largest interval on which the equation has a solution is 0 < t < 3, or (0,3).