Sr Examen
Ecuación diferencial y'''''-3y''''+3y'''-y''=0
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Solución
Ha introducido
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2 4 3 5
d d d d
- ---(y(x)) - 3*---(y(x)) + 3*---(y(x)) + ---(y(x)) = 0
2 4 3 5
dx dx dx dx
$$- \frac{d^{2}}{d x^{2}} y{\left(x \right)} + 3 \frac{d^{3}}{d x^{3}} y{\left(x \right)} - 3 \frac{d^{4}}{d x^{4}} y{\left(x \right)} + \frac{d^{5}}{d x^{5}} y{\left(x \right)} = 0$$
-y'' + 3*y''' - 3*y'''' + y''''' = 0
Respuesta
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x / x\ y(x) = C1 + C5*e + x*\C2 + (C3 + C4*x)*e /
$$y{\left(x \right)} = C_{1} + C_{5} e^{x} + x \left(C_{2} + \left(C_{3} + C_{4} x\right) e^{x}\right)$$
Clasificación
nth linear constant coeff homogeneous
nth order reducible