ODE2.1

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y''+3y'+y=0\,

Set up and solve the characteristic equation.

m^2+3m+1=0\,

m = \frac{ -3 \pm \sqrt{ 9-4 } }{2} = \frac{-3}{2} \pm \frac{\sqrt{5}}{2} = m_1, m_2\,

So the solution is

y = c_1 e^{m_1} + c_2 e^{m_2}\,

Ordinary Differential Equations

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