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Need help from someone savy with differential equtions (lemmy.ml)
submitted 5 months ago by to c/math@lemmy.ml
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So i fell upon the following differential equation : X''(t)X⁴(t)=f(t) I couldn't find anything similar on internet... Thanks in advance !

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[–] [S] 2 points 5 months ago (1 child)

Hi again ! In your reply, you told me :

this means f is a sum of exponetial

However. For the case wher f is of the form f=A•t•exp(b•t), i don't know how to convert that as a sum of exponential... I'm asking because i feel like i could just take x to be an indefinite sum of exponentials which might end up giving me some quite nice solutions... If only i could get a sum of exponentials on the other side of the equation ;)

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  • [–] 2 points 5 months ago* (last edited 5 months ago)

    Sorry, I was being a bit sloppy in the first answer. Your f=A•t•exp(b•t) term is, in general, part of the expected function space. (I just kinda forgot because in control systems, we often assume distinct real system poles for simplicity in teaching the material.)

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