Sr Examen
Ecuación diferencial a*y''-y'-b*y-c*y=0
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Solución
Ha introducido
[src]
2
d d
- --(y(x)) + a*---(y(x)) - b*y(x) - c*y(x) = 0
dx 2
dx
$$a \frac{d^{2}}{d x^{2}} y{\left(x \right)} - b y{\left(x \right)} - c y{\left(x \right)} - \frac{d}{d x} y{\left(x \right)} = 0$$
a*y'' - b*y - c*y - y' = 0
Respuesta
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/ ___________________\ / ___________________\
x*\1 - \/ 1 + 4*a*b + 4*a*c / x*\1 + \/ 1 + 4*a*b + 4*a*c /
----------------------------- -----------------------------
2*a 2*a
y(x) = C1*e + C2*e
$$y{\left(x \right)} = C_{1} e^{\frac{x \left(1 - \sqrt{4 a b + 4 a c + 1}\right)}{2 a}} + C_{2} e^{\frac{x \left(\sqrt{4 a b + 4 a c + 1} + 1\right)}{2 a}}$$
Clasificación
nth linear constant coeff homogeneous
2nd power series ordinary