Pure Mathematics

Oxford University (OX)

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College aantekeningen

FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
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13

september 2021

2021/2022
Recall that a nite sequence has the form fyngN n=0 and an innite sequence has the form fyng1 n=0. A dierence equation of order m has the form (1) yn+m = F(n; yn; yn+1; : : : ; yn+m
AXIOMATIK
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College aantekeningen

FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
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19

september 2021

2021/2022
An ordinary dierential equation of order k has the form (1) F x; y; dy dx ; d2y dx2 ; : : : ; dky dxk = 0; where F is a function of k+2 variables. We will usually write ODE as an abreviation for ordinary dierential equation. A function y(x) is a solution of the ODE (1) in the interval a < x < b if it satises the equation (1) for all x in this interval. We will usually be interested in solving an initial value problem. For an ODE of order k, this has the form Reca...
AXIOMATIK
$3.15 Meer Info