Sr Examen
Ecuación diferencial x^2*y''-x*y'+y=x/log(x)+log(x)/x
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Solución
Ha introducido
[src]
2
2 d d x log(x)
x *---(y(x)) - x*--(y(x)) + y(x) = ------ + ------
2 dx log(x) x
dx
$$x^{2} \frac{d^{2}}{d x^{2}} y{\left(x \right)} - x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} = \frac{x}{\log{\left(x \right)}} + \frac{\log{\left(x \right)}}{x}$$
x^2*y'' - x*y' + y = x/log(x) + log(x)/x
Respuesta
[src]
1 log(x)
y(x) = --- + C1*x - x*log(x) + ------ + C2*x*log(x) + x*log(x)*log(log(x))
4*x 4*x
$$y{\left(x \right)} = C_{1} x + C_{2} x \log{\left(x \right)} + x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} - x \log{\left(x \right)} + \frac{\log{\left(x \right)}}{4 x} + \frac{1}{4 x}$$
Clasificación
nth linear euler eq nonhomogeneous variation of parameters
nth linear euler eq nonhomogeneous variation of parameters Integral