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We know that y1(x) for z = (-00,00). = e-3x is a solution to the differential equation D²y - 12Dy – 45y = 0 for x = (-∞, ∞). Use the method of reduction of order to find the second solution to D²y - 12Dy - 45y = 0 (a) After you reduce the second order equation by making the substitution w = u', you get a first order equation of the form w' f(x, w) = Note: Make sure you use a lower case w, (and don't use w(t), it confuses the computer). (b) A second solution to D²y - 12Dy - 45y = 0 for x = (-∞, ∞) is Y2(x) = =

We know that y1(x) for z = (-00,00). = e-3x is a solution to the differential equation D²y - 12Dy – 45y = 0 for x = (-∞, ∞). Use the method of reduction of order to find the second solution to D²y - 12Dy - 45y = 0 (a) After you reduce the second order equation by making the substitution w = u', you get a first order equation of the form w' f(x, w) = Note: Make sure you use a lower case w, (and don't use w(t), it confuses the computer). (b) A second solution to D²y - 12Dy - 45y = 0 for x = (-∞, ∞) is Y2(x) = =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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We know that y1(x) for z = (-00,00). = e-3x is a solution to the differential equation D²y - 12Dy – 45y = 0 for x = (-∞, ∞). Use the method of reduction of order to find the second solution to D²y - 12Dy - 45y = 0 (a) After you reduce the second order equation by making the substitution w = u', you get a first order equation of the form w' f(x, w) = Note: Make sure you use a lower case w, (and don't use w(t), it confuses the computer). (b) A second solution to D²y - 12Dy - 45y = 0 for x = (-∞, ∞) is Y2(x) = =
Transcribed Image Text:We know that y1(x) for z = (-00,00). = e-3x is a solution to the differential equation D²y - 12Dy – 45y = 0 for x = (-∞, ∞). Use the method of reduction of order to find the second solution to D²y - 12Dy - 45y = 0 (a) After you reduce the second order equation by making the substitution w = u', you get a first order equation of the form w' f(x, w) = Note: Make sure you use a lower case w, (and don't use w(t), it confuses the computer). (b) A second solution to D²y - 12Dy - 45y = 0 for x = (-∞, ∞) is Y2(x) = =
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