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The general solution of the homogeneous differential equation 3x y" + 7xy + y = 0 can be written as Ye = ax- + bx where a, b are arbitrary constants and y, = 2+ 3x is a particular solution of the nonhomogeneous equation 3xy" +7xy + y = 24x + 2 By superposition, the general solution of the equation 3xy" +7xy +y = 24x + 2 is y = y, + y, so y NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) = 9, y(1) = 9 y = The fundamental theorem for linear IVPS shows that this solution is the unique solution to the IVP on the interval The Wronskian W of the fundamental set of solutions y = x and y, = x-S for the homogeneous equation is W = (2)(3x^(7/3)

The general solution of the homogeneous differential equation 3x y" + 7xy + y = 0 can be written as Ye = ax- + bx where a, b are arbitrary constants and y, = 2+ 3x is a particular solution of the nonhomogeneous equation 3xy" +7xy + y = 24x + 2 By superposition, the general solution of the equation 3xy" +7xy +y = 24x + 2 is y = y, + y, so y NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) = 9, y(1) = 9 y = The fundamental theorem for linear IVPS shows that this solution is the unique solution to the IVP on the interval The Wronskian W of the fundamental set of solutions y = x and y, = x-S for the homogeneous equation is W = (2)(3x^(7/3)

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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The general solution of the homogeneous differential equation 3x?y" + 7xy + y = 0 can be written as Ye = ax- + bx where a, b are arbitrary constants and Y, = 2 + 3x is a particular solution of the nonhomogeneous equation 3x?y" + 7xy + y = 24x + 2 By superposition, the general solution of the equation 3x?y" + 7xy + y = 24x + 2 is y = y. + y, so y NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) = 9, y(1) = 9 y = The fundamental theorem for linear IVPS shows that this solution is the unique solution to the IVP on the interval The Wronskian W of the fundamental set of solutions y = x- and y, = x-1/3 for the homogeneous equation is W = (2/(3x^(7/3))
Transcribed Image Text:The general solution of the homogeneous differential equation 3x?y" + 7xy + y = 0 can be written as Ye = ax- + bx where a, b are arbitrary constants and Y, = 2 + 3x is a particular solution of the nonhomogeneous equation 3x?y" + 7xy + y = 24x + 2 By superposition, the general solution of the equation 3x?y" + 7xy + y = 24x + 2 is y = y. + y, so y NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) = 9, y(1) = 9 y = The fundamental theorem for linear IVPS shows that this solution is the unique solution to the IVP on the interval The Wronskian W of the fundamental set of solutions y = x- and y, = x-1/3 for the homogeneous equation is W = (2/(3x^(7/3))
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