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Consider the differential equation 5e2t t² y" - 4y + 4y = = (a) Find r1, 72, roots of the characteristic polynomial of the equation above. T1, T2 = (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. y₁ (t) = Y₂ (t) = t> 0. = (c) Find the Wronskian of the fundamental solutions you found in part (b). W(t) = by ₂ (d) Use the fundamental solutions you found in (b) to find functions ₁ and such that a particular solution to the nonhomogeneous equation above is given U₁ = U2 = Yp = U₁Y₁+U₂ Y2. M M M M M 1

Consider the differential equation 5e2t t² y" - 4y + 4y = = (a) Find r1, 72, roots of the characteristic polynomial of the equation above. T1, T2 = (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. y₁ (t) = Y₂ (t) = t> 0. = (c) Find the Wronskian of the fundamental solutions you found in part (b). W(t) = by ₂ (d) Use the fundamental solutions you found in (b) to find functions ₁ and such that a particular solution to the nonhomogeneous equation above is given U₁ = U2 = Yp = U₁Y₁+U₂ Y2. M M M M M 1

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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Consider the differential equation 5e2t t² y" - 4y + 4y = = (a) Find r1, 72, roots of the characteristic polynomial of the equation above. T1, T2 = (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. y₁ (t) = Y₂ (t) = t> 0. = (c) Find the Wronskian of the fundamental solutions you found in part (b). W(t) = by (d) Use the fundamental solutions you found in (b) to find functions ₁ and ₂ such that a particular solution to the nonhomogeneous equation above is given U₁ = U2 = Yp = U₁Y₁+U₂ Y2. M M M M M M
Transcribed Image Text:Consider the differential equation 5e2t t² y" - 4y + 4y = = (a) Find r1, 72, roots of the characteristic polynomial of the equation above. T1, T2 = (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. y₁ (t) = Y₂ (t) = t> 0. = (c) Find the Wronskian of the fundamental solutions you found in part (b). W(t) = by (d) Use the fundamental solutions you found in (b) to find functions ₁ and ₂ such that a particular solution to the nonhomogeneous equation above is given U₁ = U2 = Yp = U₁Y₁+U₂ Y2. M M M M M M
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