Solve the equation [itex]m\frac{d^{2}x}{dt^{2}} + c\frac{dx}{dt} + kx = (ax + b)^{2} + c^{2}[/itex] for the constants [itex]m, c, k[/itex](adsbygoogle = window.adsbygoogle || []).push({});

The right hand side a, b, and c are arbitrary digits. For me they are a = 2, b = 3, and c = 8.

The problem recommends creating a linear system of equations for me to solve. This is to be done using MapleSoft.

I tried making a set of equations using (m*r^2 + c*r + k) = (2+3)^2 + 64 and then using various values of r to get a system of equations. But the result got me [itex]m = 0, c = 0[/itex] and k equaling some number. However this is incorrect because the left part of the main equations with the constants will be used to make a vibration model that I would solve. With m and c equaling 0, I would not have any derivatives and therefore not being able to solve the equation.

So now I'm at a loss. I also tried converting the equation into 2 systems of first order differentials but that lead to me really nowhere.

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# Linear system of equations for a differential equation

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