Hi there.(adsbygoogle = window.adsbygoogle || []).push({});

I've been struggling with this problem for days now (4 days, no joke) and I feel like I have a mental block and really cannot get any further.

I have a system that's described by

[tex] f(t) = g''(t) + 15g'(t) + 1600g(t) [/tex] Where the input is [tex]g(t)[/tex]

The problem is to, with this information, determine the coefficients in another system, where the input is[tex]f(t)[/tex]and the output is given by [tex]u(t)[/tex], so that [tex]u(t) = g(t)[/tex]

This other system is given by

[tex]c_2u''(t)+c_1u'(t)+c_0u(t) = b_2f''(t) + b_1f'(t) + b_0f(t)[/tex]

I think this is supposed to be simple and I think I make it more difficult in my head than it is. I first substituted f(t) in the second differential equation with the left hand side of the first equation:

[tex]c_2u''(t)+c_1u'(t)+c_0u(t) = b_2f''(t) + b_1f'(t) + b_0(g''(t) + 15g'(t) + 1600g(t))[/tex]

[tex]=> c_2u''(t)+c_1u'(t)+c_0u(t) = b_2f''(t) + b_1f'(t) + b_0g''(t) + b_015g'(t) + b_01600g(t)[/tex]

I´m supposed to get numerical values for all coefficients but I really can’t figure out what coefficients makes u(x) = g(t). I don't really know how to proceed. I've tried a lot of other ways too, for example solve for u(t) and g(t) explicitly:

[tex]u(t) = \frac{b_2}{c_0}f''(t) + \frac{b_1}{c_0}f'(t) + \frac{b_0}{c_0}f(t)-\frac{c_2}{c_0}u''(t)-\frac{c_1}{c_0}u'(t)[/tex] and [tex] g(t) = \frac{1}{1600}g''(t) + \frac{15}{1600}g'(t) -\frac{1}{1600}f(t)[/tex]

And then putting their right hand sides equal each other, but this didn't really get me anywhere.

Just before posting this question I’ve been starring and trying for another 4 hours, and I feel I’m that my self-confidence is at an all-time low and I'm starting to ask myself if I really should be doing math at all (Yes, it's really a first world issue, I know).

REALLY grateful for any help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Determine coefficients of a differential equation

Loading...

Similar Threads for Determine coefficients differential |
---|

A Solving linear 2nd order IVP non-constant coefficient |

I Heat equation with variable coefficients |

I Second order PDE with variable coefficients |

A A system of DEs with variable coefficients. |

**Physics Forums | Science Articles, Homework Help, Discussion**