a. Show the left side is zero. b. y2 = tet с. (0, оо) (0, 00) 1 d. y = 2t -tet e

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Can someone show me how to end up to these solutions?

7.
a. Show the left side is zero.
b. y2 = tet
(0, 00)
с.
d. y = 2t –te
Transcribed Image Text:7. a. Show the left side is zero. b. y2 = tet (0, 00) с. d. y = 2t –te
7. Consider the DE ty" – t(t + 2)y' + (t + 2)y = 0
(a) Verify that y(t) = t is a solution to the DE.
(b) Use reduction of order to find the second solution for the fundamental set for this
DE.
(c) Given initial conditions y(1) = 1, y'(1)
unique solution is guaranteed to exist by applying the appropriate existence/uniqueness
0, find the largest interval on which a
theorem.
(d) Solve the IVP given initial conditions y(1) = 1, y'(1) = 0.
Transcribed Image Text:7. Consider the DE ty" – t(t + 2)y' + (t + 2)y = 0 (a) Verify that y(t) = t is a solution to the DE. (b) Use reduction of order to find the second solution for the fundamental set for this DE. (c) Given initial conditions y(1) = 1, y'(1) unique solution is guaranteed to exist by applying the appropriate existence/uniqueness 0, find the largest interval on which a theorem. (d) Solve the IVP given initial conditions y(1) = 1, y'(1) = 0.
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