Consider the differential equation y'' + 2y' + 50y = 0. (a) Verify that y₁ = e Y2 = e sin (7x) are solutions. X y = (b) Use constants c₁ and c₂ to write the most general solution. You may use an underscore _ to write subscripts. Y X c₁e = cos(7x) and (c) Find the solution which satisfies y(0) y'(0) = - 2. X X sin (7x) + c₂e- cos (7x) ✓ - 6 and
Consider the differential equation y'' + 2y' + 50y = 0. (a) Verify that y₁ = e Y2 = e sin (7x) are solutions. X y = (b) Use constants c₁ and c₂ to write the most general solution. You may use an underscore _ to write subscripts. Y X c₁e = cos(7x) and (c) Find the solution which satisfies y(0) y'(0) = - 2. X X sin (7x) + c₂e- cos (7x) ✓ - 6 and
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**
\( y'' + 2y' + 50y = 0. \)
**(a)** Verify that \( y_1 = e^{-x} \cos(7x) \) and \( y_2 = e^{-x} \sin(7x) \) are solutions.
**(b)** Use constants \( c_1 \) and \( c_2 \) to write the most general solution. *You may use an underscore _ to write subscripts.*
\[ y = c_1 e^{-x} \sin(7x) + c_2 e^{-x} \cos(7x) \checkmark \]
**(c)** Find the solution which satisfies \( y(0) = 6 \) and \( y'(0) = -2 \).
\[ y = \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff57c5c9b-acb3-4a3d-a39b-55eeff7ee4ad%2F0dea45c3-b16f-4ed6-883e-b20c5286c443%2Fwsxhbwq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Consider the differential equation**
\( y'' + 2y' + 50y = 0. \)
**(a)** Verify that \( y_1 = e^{-x} \cos(7x) \) and \( y_2 = e^{-x} \sin(7x) \) are solutions.
**(b)** Use constants \( c_1 \) and \( c_2 \) to write the most general solution. *You may use an underscore _ to write subscripts.*
\[ y = c_1 e^{-x} \sin(7x) + c_2 e^{-x} \cos(7x) \checkmark \]
**(c)** Find the solution which satisfies \( y(0) = 6 \) and \( y'(0) = -2 \).
\[ y = \]
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