Sr Examen
Ecuación diferencial y'''-4y''+7y'-6y=0
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Solución
Ha introducido
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2 3
d d d
-6*y(x) - 4*---(y(x)) + 7*--(y(x)) + ---(y(x)) = 0
2 dx 3
dx dx
$$- 6 y{\left(x \right)} + 7 \frac{d}{d x} y{\left(x \right)} - 4 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$$
-6*y + 7*y' - 4*y'' + y''' = 0
Respuesta
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/ x / ___\ / ___\\ x y(x) = \C1*e + C2*sin\x*\/ 2 / + C3*cos\x*\/ 2 //*e
$$y{\left(x \right)} = \left(C_{1} e^{x} + C_{2} \sin{\left(\sqrt{2} x \right)} + C_{3} \cos{\left(\sqrt{2} x \right)}\right) e^{x}$$
Clasificación
nth linear constant coeff homogeneous