How to Write a Linear System in Matrix Form

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Homework Statement


Write the given system in the form x'=P(t)x + f(t)

x'=-3y , y'=3x


Homework Equations


x'=P(t)x + f(t)
x(t)=c_1x_1(t)+c_2x_2(t)+...+c_nx_n(t)

The Attempt at a Solution


I have no idea how to start this since my teacher never covered this in our notes and the book doesn't give an example of this type of problem. Please help!
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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