(b) Based on an inspection of the direction field, describe how solutions behave for large t. O All solutions seem to approach a line in the region where the negative and positive slopes meet each other. O All solutions seem to eventually have positive slopes, and hence increase without bound. O All solutions seem to eventually have negative slopes, and hence decrease without bound. O The solutions appear to be oscillatory. O If y(0) > 0, solutions appear to eventually have positive slopes, and hence increase without bound. If y(0) ≤ 0, solutions appear to have negative slopes and decrease without bound. (c) Find the general solution of the given differential equation. y(t) = Use it to determine how solutions behave as t → 00. O All solutions converge to the function y = O All solutions will increase exponentially. O All solutions converge to the function y = O All solutions converge to the function y = O All solutions will decrease exponentially. cos 2t. sin 2t.
(b) Based on an inspection of the direction field, describe how solutions behave for large t. O All solutions seem to approach a line in the region where the negative and positive slopes meet each other. O All solutions seem to eventually have positive slopes, and hence increase without bound. O All solutions seem to eventually have negative slopes, and hence decrease without bound. O The solutions appear to be oscillatory. O If y(0) > 0, solutions appear to eventually have positive slopes, and hence increase without bound. If y(0) ≤ 0, solutions appear to have negative slopes and decrease without bound. (c) Find the general solution of the given differential equation. y(t) = Use it to determine how solutions behave as t → 00. O All solutions converge to the function y = O All solutions will increase exponentially. O All solutions converge to the function y = O All solutions converge to the function y = O All solutions will decrease exponentially. cos 2t. sin 2t.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please answer the two pictures. They are connected ty.
Transcribed Image Text:(b) Based on an inspection of the direction field, describe how solutions behave for large t.
O All solutions seem to approach a line in the region where the negative and positive slopes meet each other.
O All solutions seem to eventually have positive slopes, and hence increase without bound.
O All solutions seem to eventually have negative slopes, and hence decrease without bound.
O The solutions appear to be oscillatory.
O If y(0) > 0, solutions appear to eventually have positive slopes, and hence increase without bound. If y(0) ≤ 0, solutions appear to have negative slopes and decrease without bound.
(c) Find the general solution of the given differential equation.
y(t) =
Use it to determine how solutions behave as too.
O All solutions converge to the function y = cos 2t.
O All solutions will increase exponentially.
O All solutions converge to the function y =
O All solutions converge to the function y =
O All solutions will decrease exponentially.
sin 2t.
Transcribed Image Text:Consider the following differential equation. (A computer algebra system is recommended.)
y' + = 7 cos 2t, t> 0
1/2 t
(a) Draw a direction field for the given differential equation.
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