Sr Examen
Ecuación diferencial x^(2)(2x-1)y’’-2x(5x-3)y’+6(x-1)y=0
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Solución
Ha introducido
[src]
2
2 d d
(-6 + 6*x)*y(x) + x *(-1 + 2*x)*---(y(x)) - 2*x*(-3 + 5*x)*--(y(x)) = 0
2 dx
dx
$$x^{2} \left(2 x - 1\right) \frac{d^{2}}{d x^{2}} y{\left(x \right)} - 2 x \left(5 x - 3\right) \frac{d}{d x} y{\left(x \right)} + \left(6 x - 6\right) y{\left(x \right)} = 0$$
x^2*(2*x - 1)*y'' - 2*x*(5*x - 3)*y' + (6*x - 6)*y = 0
Respuesta
[src]
/ ___ \
___ | _ / ___ ___ | \ 2*\/ 6 _ / ___ ___ | \|
3 \/ 6 | |_ |-2 - \/ 6 , -2 - \/ 6 | 2*x | / 2*x \ |_ |-2 + \/ 6 , -2 + \/ 6 | 2*x ||
x*(-1 + 2*x) *(-1 + 2*x) *|C2* | | | 1 - --------| + C1*|1 - --------| * | | | 1 - --------||
| 2 1 | ___ | -1 + 2*x| \ -1 + 2*x/ 2 1 | ___ | -1 + 2*x||
\ \ 1 - 2*\/ 6 | / \ 1 + 2*\/ 6 | //
y(x) = -------------------------------------------------------------------------------------------------------------------------------------------------------
-1/2 + x
$$y{\left(x \right)} = \frac{x \left(2 x - 1\right)^{3} \left(2 x - 1\right)^{\sqrt{6}} \left(C_{1} \left(- \frac{2 x}{2 x - 1} + 1\right)^{2 \sqrt{6}} {{}_{2}F_{1}\left(\begin{matrix} -2 + \sqrt{6}, -2 + \sqrt{6} \\ 1 + 2 \sqrt{6} \end{matrix}\middle| {- \frac{2 x}{2 x - 1} + 1} \right)} + C_{2} {{}_{2}F_{1}\left(\begin{matrix} - \sqrt{6} - 2, - \sqrt{6} - 2 \\ 1 - 2 \sqrt{6} \end{matrix}\middle| {- \frac{2 x}{2 x - 1} + 1} \right)}\right)}{x - \frac{1}{2}}$$
Clasificación
2nd hypergeometric
2nd hypergeometric Integral
2nd power series regular