Sr Examen
Ecuación diferencial xyy’’+(y^2)-yy’=0
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Solución
Ha introducido
[src]
2
2 d d
y (x) - --(y(x))*y(x) + x*---(y(x))*y(x) = 0
dx 2
dx
$$x y{\left(x \right)} \frac{d^{2}}{d x^{2}} y{\left(x \right)} + y^{2}{\left(x \right)} - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x*y*y'' + y^2 - y*y' = 0
Respuesta
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/ / ___\ / ___\\ y(x) = x*\C1*besselj\2, 2*\/ x / + C2*bessely\2, 2*\/ x //
$$y{\left(x \right)} = x \left(C_{1} J_{2}\left(2 \sqrt{x}\right) + C_{2} Y_{2}\left(2 \sqrt{x}\right)\right)$$
Clasificación
factorable
2nd linear bessel
2nd power series regular