Second order differential equation

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SUMMARY

The forum discussion centers on solving the second-order differential equation y'' + 4y' + 4y = 0. A key suggestion is to use the trial solution y = e^(mx) for equations with constant coefficients. This method is essential for finding the general solution of such differential equations. The equation can be factored to identify the characteristic roots, leading to a complete solution.

PREREQUISITES
  • Understanding of second-order differential equations
  • Familiarity with constant coefficients in differential equations
  • Knowledge of trial solutions in differential equations
  • Basic algebra for factoring polynomials
NEXT STEPS
  • Study the method of characteristic equations for second-order differential equations
  • Learn about the application of trial solutions in solving differential equations
  • Explore the implications of repeated roots in characteristic equations
  • Investigate the use of the exponential function in differential equations
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Students and professionals in mathematics, engineering, and physics who are working with differential equations, particularly those focusing on second-order linear equations with constant coefficients.

Mugged
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Hi, i need help solving this equation:

[tex]y'' + 4y' + 4y = 0[/tex]

any help is appreciated!
 
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Mugged said:
Hi, i need help solving this equation:

[tex]y'' + 4y' + 4y = 0[/tex]

any help is appreciated!

What attempt have you made?

Here is a hint: For a 2nd order DE with constant coefficients, try using y=emx as a trial solution.
 

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