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Ecuaciones diferenciales/ x*y''-(1+2x*ctg(x))y'+(ctg(x)+2x*(ctg(x))^2+x)y-2x^3*sin(x)

Ecuación diferencial x*y''-(1+2x*ctg(x))y'+(ctg(x)+2x*(ctg(x))^2+x)y-2x^3*sin(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                                                                                      
   d          /           2            \                         d             3           
x*---(y(x)) + \x + 2*x*cot (x) + cot(x)/*y(x) - (1 + 2*x*cot(x))*--(y(x)) - 2*x *sin(x) = 0
    2                                                            dx                        
  dx
$$- 2 x^{3} \sin{\left(x \right)} + x \frac{d^{2}}{d x^{2}} y{\left(x \right)} - \left(2 x \cot{\left(x \right)} + 1\right) \frac{d}{d x} y{\left(x \right)} + \left(2 x \cot^{2}{\left(x \right)} + x + \cot{\left(x \right)}\right) y{\left(x \right)} = 0$$ 
-2*x^3*sin(x) + x*y'' - (2*x*cot(x) + 1)*y' + (2*x*cot(x)^2 + x + cot(x))*y = 0
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