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May 21st, 2019, 06:10 PM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 825 Thanks: 113 Math Focus: Elementary Math  Differential equation
$\displaystyle \frac{d^4 z}{dt^4 }=z+C \; $ , Cconstant . To get at least one solution , apply derivatives to equallity : $\displaystyle z^{(5)}=z'$ , How to get the general solution ? Last edited by idontknow; May 21st, 2019 at 06:17 PM. 
May 21st, 2019, 07:38 PM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,340 Thanks: 983 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
$\displaystyle \dfrac{d^4 z}{dt^4}  z = 0$ The characteristic equation is $\displaystyle m^4  1 = 0$, which has solutions 1, 1, i, i. Thus the homogeneous solution is of the form: $\displaystyle z_h(t) = Ae^t + Be^{t} + D~\sin(t) + E~\cos(t)$. Or, if you prefer $\displaystyle z_h(t) = Ae^t + Be^{1} + De^{it} + Ee^{it}$ (The D's and E's are different from each other in the two equations.) Can you finish? Dan Last edited by skipjack; May 22nd, 2019 at 01:07 AM.  

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