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Ecuaciones diferenciales/ x^2*ln^(2)(x)*y"-x*ln(x)*(ln(x)+2)*y'+2*(ln(x)+1)*y=2*ln^3(x)

Ecuación diferencial x^2*ln^(2)(x)*y"-x*ln(x)*(ln(x)+2)*y'+2*(ln(x)+1)*y=2*ln^3(x)

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Para el problema de Cauchy:

y() =
y'() =
y''() =
y'''() =
y''''() =

Gráfico:

interior superior
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Solución

Ha introducido [src] 
                                   2                                                   
                       2    2     d                         d                      3   
(2 + 2*log(x))*y(x) + x *log (x)*---(y(x)) - x*(2 + log(x))*--(y(x))*log(x) = 2*log (x)
                                   2                        dx                         
                                 dx
$$x^{2} \log{\left(x \right)}^{2} \frac{d^{2}}{d x^{2}} y{\left(x \right)} - x \left(\log{\left(x \right)} + 2\right) \log{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \left(2 \log{\left(x \right)} + 2\right) y{\left(x \right)} = 2 \log{\left(x \right)}^{3}$$ 
x^2*log(x)^2*y'' - x*(log(x) + 2)*log(x)*y' + (2*log(x) + 2)*y = 2*log(x)^3
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