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Let Vi (t) = e2", V½(t) = t e2t, V3(t) = t²e2+. (1) Verify that V1(t), V½(t) and V3(t) solve v" – 6v" + 12v' – 8v = 0. (2) Compute the Wronskian Wr[V1, V2, V3](t). (Evaluate the determinant and simplify.) Verify that it satisfies w' – 6w = 0. - (3) Solve the general initial-value problem v" – 6v" + 12v' – 8v = 0, = vo , v(0) = v1 , v"(0) = v2 .

Let Vi (t) = e2", V½(t) = t e2t, V3(t) = t²e2+. (1) Verify that V1(t), V½(t) and V3(t) solve v" – 6v" + 12v' – 8v = 0. (2) Compute the Wronskian Wr[V1, V2, V3](t). (Evaluate the determinant and simplify.) Verify that it satisfies w' – 6w = 0. - (3) Solve the general initial-value problem v" – 6v" + 12v' – 8v = 0, = vo , v(0) = v1 , v"(0) = v2 .

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let Vi (t) = e2", V½(t) = t e2t, V3(t) = t²e2+. (1) Verify that V1(t), V½(t) and V3(t) solve v" – 6v" + 12v' – 8v = 0. (2) Compute the Wronskian Wr[V1, V2, V3](t). (Evaluate the determinant and simplify.) Verify that it satisfies w' – 6w = 0. - (3) Solve the general initial-value problem v" – 6v" + 12v' – 8v = 0, = vo , v(0) = v1 , v"(0) = v2 .
Transcribed Image Text:Let Vi (t) = e2", V½(t) = t e2t, V3(t) = t²e2+. (1) Verify that V1(t), V½(t) and V3(t) solve v" – 6v" + 12v' – 8v = 0. (2) Compute the Wronskian Wr[V1, V2, V3](t). (Evaluate the determinant and simplify.) Verify that it satisfies w' – 6w = 0. - (3) Solve the general initial-value problem v" – 6v" + 12v' – 8v = 0, = vo , v(0) = v1 , v"(0) = v2 .
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