How Do You Choose Initial Conditions for Coupled Linear Differential Equations?

sssspppp
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Hi

can anyone tell me how I can chose/investigate some sensible initial condition for a coupled linear system of linear differential equations?

x*=Ax where (x1(0) x2(0))=(a,b)

Thank you
 
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sssspppp said:
Hi

can anyone tell me how I can chose/investigate some sensible initial condition for a coupled linear system of linear differential equations?

x*=Ax where (x1(0) x2(0))=(a,b)

Thank you
Can you clarify what you're asking?
 

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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