Sr Examen
Ecuación diferencial y'''''+4y''''+5y'''-6y'-4y=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
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4 3 5
d d d d
- 6*--(y(x)) - 4*y(x) + 4*---(y(x)) + 5*---(y(x)) + ---(y(x)) = 0
dx 4 3 5
dx dx dx
$$- 4 y{\left(x \right)} - 6 \frac{d}{d x} y{\left(x \right)} + 5 \frac{d^{3}}{d x^{3}} y{\left(x \right)} + 4 \frac{d^{4}}{d x^{4}} y{\left(x \right)} + \frac{d^{5}}{d x^{5}} y{\left(x \right)} = 0$$
-4*y - 6*y' + 5*y''' + 4*y'''' + y''''' = 0
Respuesta
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-2*x x -x y(x) = C4*e + C5*e + (C1 + C2*sin(x) + C3*cos(x))*e
$$y{\left(x \right)} = C_{4} e^{- 2 x} + C_{5} e^{x} + \left(C_{1} + C_{2} \sin{\left(x \right)} + C_{3} \cos{\left(x \right)}\right) e^{- x}$$
Clasificación
nth linear constant coeff homogeneous