Matlab: Estimating coefficients of nonlinear differential equations
<p>Need to solve the system of nonlinear differential equations:</p>

<pre><code>x1p = a1*u2*x1^1.3 + a2*u1 + a3*u3
x2p = (a4*u2 + a5)*x1^1.3 + a6*x2
x3p = (a7*u3 + (a8*u2-a9)*x1)/a10
</code></pre>

<p>x1p, x2p &amp; x3p are time derivatives of x1, x2 &amp; x3, i.e. dx1/dt, dx2/dt &amp; dx3/dt.</p>

<p>we have descrete data of x1, x2 &amp; x3 as well as of u1, u2 &amp; u3. We need to solve the problem in order to get the unknown coefficients, a1, a2, …, a10.</p>

<p>Have checked many posts and can say the solution involves ODE45 (or other ODEX) and probably fsolve or fminsearch (Matlab), but have not managed to setup up the problem correctly, guess we don't understand the coding well. Please, suggestions. </p>