Sr Examen
Ecuación diferencial x^3y'''+5x^2y''+7xy'+8y=0
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Solución
Ha introducido
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3 2
3 d 2 d d
8*y(x) + x *---(y(x)) + 5*x *---(y(x)) + 7*x*--(y(x)) = 0
3 2 dx
dx dx
$$x^{3} \frac{d^{3}}{d x^{3}} y{\left(x \right)} + 5 x^{2} \frac{d^{2}}{d x^{2}} y{\left(x \right)} + 7 x \frac{d}{d x} y{\left(x \right)} + 8 y{\left(x \right)} = 0$$
x^3*y''' + 5*x^2*y'' + 7*x*y' + 8*y = 0
Respuesta
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C1
y(x) = -- + C2*sin(2*log(x)) + C3*cos(2*log(x))
2
x
$$y{\left(x \right)} = \frac{C_{1}}{x^{2}} + C_{2} \sin{\left(2 \log{\left(x \right)} \right)} + C_{3} \cos{\left(2 \log{\left(x \right)} \right)}$$
Clasificación
nth linear euler eq homogeneous