Examples of differential equations: Difference between revisions

Revision as of 06:21, 3 March 2021

Revision as of 12:48, 19 March 2021

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: <math>m\lambda^2 + c \lambda + k = 0. </math>

This is a [[quadratic equation]] which we can solve. If <math>c^2<4km</math> there are two complex conjugate roots ''a''&nbsp;±&nbsp;''ib'', and the solution (with the above boundary conditions) will look like this:

: <math>x(t) = e^{at} \left(\cos bt - \frac{a}{b} \sin bt \right) </math>

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<syntaxhighlight lang="matlab">

x = dsolve('D2x+c*Dx+k*x=0','x(0)=1','Dx(0)=0')

% or equivalently

syms x(t) c k

Dx = diff(x, t);

x = dsolve(diff(x,t,2) + c*Dx + k*x == 0, x(0) == 1, Dx(0) == 0)

</syntaxhighlight>

although the solution looks rather ugly,