University Homework Problem

[proper fiber]

tried everything I could think of, cant find a way to deal with the cosh properly,
everything either ends up way too complex or just flat out doesnt work, tried variation of parameters and "guessing" the particular soln using this chart:
https://image3.slideserve.com/5734172/rule-of-case-1-l.jpg
to no avail 😭

[jaunty elk]

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[hoary egret]

A way you can do it is setting sin(sqrt(3)x)=(e^sqrt(3)ix-e^-sqrt(3)ix)/2i and cosh(sqrt(3)x)=(e^sqrt(3)x+e^-sqrt(3)x)/2 multiply all of these exponential terms together ( you’ll get expressions with exponentials ) and you can use a method called superposition of variables where you solve the DE for one of the exponential terms (solving y’’’’ +18y’’+81y=e^ax and g’’’’+18g’’+81g=e^bx then adding both solutions will give a particular solution to the initial DE for example)

[proper fiber]

ill give that a shot, leaving the house rn but sounds promising ill try it when im back

[hoary egret]

Ok good luck