Sr Examen
Ecuación diferencial x^3y'''-3x^2y''+2xy'-y=0
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Solución
Ha introducido
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3 2
3 d 2 d d
-y(x) + x *---(y(x)) - 3*x *---(y(x)) + 2*x*--(y(x)) = 0
3 2 dx
dx dx
$$x^{3} \frac{d^{3}}{d x^{3}} y{\left(x \right)} - 3 x^{2} \frac{d^{2}}{d x^{2}} y{\left(x \right)} + 2 x \frac{d}{d x} y{\left(x \right)} - y{\left(x \right)} = 0$$
x^3*y''' - 3*x^2*y'' + 2*x*y' - y = 0
Respuesta
[src]
/ 3 2 \ / 3 2 \ / 3 2 \
CRootOf\x - 6*x + 7*x - 1, 0/ CRootOf\x - 6*x + 7*x - 1, 1/ CRootOf\x - 6*x + 7*x - 1, 2/
y(x) = C1*x + C2*x + C3*x
$$y{\left(x \right)} = C_{1} x^{\operatorname{CRootOf} {\left(x^{3} - 6 x^{2} + 7 x - 1, 0\right)}} + C_{2} x^{\operatorname{CRootOf} {\left(x^{3} - 6 x^{2} + 7 x - 1, 1\right)}} + C_{3} x^{\operatorname{CRootOf} {\left(x^{3} - 6 x^{2} + 7 x - 1, 2\right)}}$$
Clasificación
nth linear euler eq homogeneous