- #1

chaksome

- 17

- 6

- Homework Statement:
- Second order ODE

- Relevant Equations:
- x‘’(t)+4x’(t)+8x(t) = f(t)

I wish to know if there is a method to work out x(t).

[No matter which form f(t) is]

Thank you~

[No matter which form f(t) is]

Thank you~

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- Thread starter chaksome
- Start date

- #1

chaksome

- 17

- 6

- Homework Statement:
- Second order ODE

- Relevant Equations:
- x‘’(t)+4x’(t)+8x(t) = f(t)

I wish to know if there is a method to work out x(t).

[No matter which form f(t) is]

Thank you~

[No matter which form f(t) is]

Thank you~

- #2

- #3

- #4

BvU

Science Advisor

Homework Helper

- 15,177

- 4,202

It gives you a formal, general method to find a solution, yes.

- #5

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 970

Now use "variation of parameters". We look for a solution to the entire equation of the form [itex]y(x)= e^{-4x}\left(u(x)e^{2x\sqrt{3}}+ v(x)e^{-2x\sqrt{3}}\right)[/itex]. That is, we let the "parameters", A and B, vary. Surely That method is given in your textbook. You can also read about it at http://tutorial.math.lamar.edu/Classes/DE/VariationofParameters.aspx.

The calculations are tedious but doable! The result will be an integral in f(x) that you add to the general solution to the homogeneous equation.

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