Sr Examen
Ecuación diferencial y'''-3y''+3y'-6y=0
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Solución
Ha introducido
[src]
2 3
d d d
-6*y(x) - 3*---(y(x)) + 3*--(y(x)) + ---(y(x)) = 0
2 dx 3
dx dx
$$- 6 y{\left(x \right)} + 3 \frac{d}{d x} y{\left(x \right)} - 3 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$$
-6*y + 3*y' - 3*y'' + y''' = 0
Respuesta
[src]
/ 3 ___\ / 3 ___\
| \/ 5 | | \/ 5 |
/ 3 ___\ x*|1 - -----| / ___ 3 ___\ / ___ 3 ___\ x*|1 - -----|
x*\1 + \/ 5 / \ 2 / |x*\/ 3 *\/ 5 | |x*\/ 3 *\/ 5 | \ 2 /
y(x) = C3*e + C1*e *sin|-------------| + C2*cos|-------------|*e
\ 2 / \ 2 /
$$y{\left(x \right)} = C_{1} e^{x \left(1 - \frac{\sqrt[3]{5}}{2}\right)} \sin{\left(\frac{\sqrt{3} \sqrt[3]{5} x}{2} \right)} + C_{2} e^{x \left(1 - \frac{\sqrt[3]{5}}{2}\right)} \cos{\left(\frac{\sqrt{3} \sqrt[3]{5} x}{2} \right)} + C_{3} e^{x \left(1 + \sqrt[3]{5}\right)}$$
Clasificación
nth linear constant coeff homogeneous