Solving y(4)-4y" = 16e2x: Need Help!

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  • Thread starter Thread starter lizlemon1991
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SUMMARY

The discussion focuses on solving the differential equation y(4) - 4y" = 16e^(2x). The initial approach involves substituting w = y" and w" = y(4) to simplify the problem. Participants emphasize the necessity of finding both the homogeneous and particular solutions, with the characteristic equation being a critical tool for determining the homogeneous solution.

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  • Understanding of fourth-order differential equations
  • Familiarity with characteristic equations
  • Knowledge of homogeneous and particular solutions
  • Basic skills in differential calculus
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  • Study the method for solving fourth-order differential equations
  • Learn how to derive the characteristic equation for differential equations
  • Research techniques for finding homogeneous solutions
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Students in advanced mathematics, particularly those studying differential equations, as well as educators and tutors seeking to clarify methods for solving complex equations.

lizlemon1991
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I'm working on this equation and I think I remember how to do it, but my notes from this class are so scattered and I can't seem to find the section in my textbook.

the problem is:

y(4)-4y" = 16e2x

can someone help me out with just getting started? Doesn't it have something to do with letting w=y" and w"=y4?
 
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You need to get the homogeneous solution and the particular solution.
To obtain the homogeneous solution use the characteristic equation.
 

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