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#### ognik

##### Active member

- Feb 3, 2015

- 471

Char. Eqtn. is $p^2 + 2p + 3 = 0, \therefore p = 1 \pm i \sqrt{2}$

Solutions of the form $p=r \pm iq$ are $y = e^{rx} \left( C_1 Cos qx + c_2 Sin qx \right) $

$\therefore y = e^{x} \left( C_1 Cos qx + c_2 Sin qx \right) , q= \sqrt2$

Now $y' = e^{x}\left( - C_1q Sin qx + C_2q Cos qx + C_1 Cos qx + C_2 Sin qx \right)$

$ y(0) = 0 = C_1, y'(0) = 1 = C_2q + C_1, \therefore C_2 = \frac{1}{\sqrt 2}$

Is that right please?