I was given this problem in a homework set and I don't know where to start -- haven't done diff equation in a while, so any help would be very appreciated!! For small fluctuations of light, the photo-receptor can be considered linear and the equation describing its response is: $$\frac+1.5\frac+0.5~x(t)=6s$$ where $s$ is the light intensity (millenniums/mm $^2$ ) and $x(t)$ is the firing rate of the photo-receptor (Hz). Note that $s$ and $x$ are measured with respect to their nominal values, so $s = 0$ corresponds to normal illumination and the firing rate $x = 0$ is the deviation from some non-zero firing rate corresponding to normal illumination. How do I convert this second order ODE into a system of two first order ODEs by defining the second state variable as $y(t)=\frac $ (rate of change of firing rate $x(t)~$ ? Any advice or explanation would be very appreciated. Thank you!
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