how to get Parameters of nonlinear function by passing pairs of values to it

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Bass Tea
Bass Tea 2021-7-9
编辑： Bass Tea 2021-7-10
hey there,
i have another stupido question =) :
imaging i've got a polynomial function like this
i can retrieve by using 3 pairs of values got from auxilliary points like with following equation system...
(edit 1): and this is vectorial notation...
; ; leads to and so
% code to doing so:
syms C1 C2 C3; A=[0 0 1;4 2 1;16 4 1]; t=[C1;C2;C3]; b=[0;6;7]; t=A^(-1)*b
So far so good.
But now, i'm analysing a coast down experiment. My differential equation is like this , where n is meant to be the rotational speed of driving wheels in , t is time in and are coefficients, based on resitive torques from rolling resistance, acceleration resistance, air drag and so on. When i put it into MATLAB i got the solution
.
So far so good. Now, theoretically, when i drive a test run on the road and want to point out , i'm logging speed over time. So i have tons of data pairs to determine .
But how can i extract this from that differential equation solution?
% code to experiment
clear; close all; format shortG
syms n(t) A B C D;
eqn = diff(n,t,1) == -A/D*n^2 - B/D*n - C/D
cond = n(0) == 950/60; % start speed 950 [rpm] into [rps]
...nSol(t) = dsolve(eqn,cond,'Implicit', true)
nSol(t) = dsolve(eqn,cond)
nSol = simplify(nSol)
many thanks
Basti :)
edit1: added auxilliary step for equation system 1

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