Sr Examen
Ecuación diferencial ydx-4(xy+y6)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d d
- 4*y6*--(y(x)) - 4*x*--(y(x))*y(x) + y(x) = 0
dx dx
$$- 4 x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 4 y_{6} \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} = 0$$
-4*x*y*y' - 4*y6*y' + y = 0
Respuesta
[src]
/ / 7 2 15*C1\ \
| 3 2 2 / 2\ C1*|- -- - 6*C1 + -----| 2 2 |
5 | 1 4 21*C1 5*C1 11*C1 3*C1 *(-1 + 4*C1) C1*(1 - 8*C1) C1*\1 - 40*C1 + 96*C1 / \ 32 4 / C1 *(9/4 - 6*C1) C1*(-5/8 + 3*C1) C1*(-3/8 + 3*C1) C1 *(1 - 8*C1) 3*C1*(-1 + 4*C1)|
2 C1*x *|---- + 6*C1 - ------ - ---- + ------ - ----------------- - ------------- - ----------------------- + ------------------------- + ---------------- + ---------------- + ---------------- + -------------- + ----------------| 3 / 2\ 4 / 3 2 \
C1*x C1*x *(1 - 4*C1) \1024 4 128 16 16 128 256 4 4 16 16 32 128 / C1*x *\1 - 20*C1 + 32*C1 / C1*x *\1 - 384*C1 - 40*C1 + 288*C1 - 4*C1*(1 - 8*C1) + 24*C1*(-1 + 4*C1)/ / 6\
y(x) = C1 + ---- + ---------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------- + --------------------------------------------------------------------------- + O\x /
4*y6 2 5 3 4
32*y6 120*y6 384*y6 6144*y6
$$y{\left(x \right)} = C_{1} + \frac{C_{1} x}{4 y_{6}} + \frac{C_{1} x^{2} \left(1 - 4 C_{1}\right)}{32 y_{6}^{2}} + \frac{C_{1} x^{3} \left(32 C_{1}^{2} - 20 C_{1} + 1\right)}{384 y_{6}^{3}} + \frac{C_{1} x^{4} \left(- 384 C_{1}^{3} + 288 C_{1}^{2} - 4 C_{1} \left(1 - 8 C_{1}\right) + 24 C_{1} \left(4 C_{1} - 1\right) - 40 C_{1} + 1\right)}{6144 y_{6}^{4}} + \frac{C_{1} x^{5} \left(6 C_{1}^{4} - \frac{21 C_{1}^{3}}{4} + \frac{C_{1}^{2} \left(1 - 8 C_{1}\right)}{32} + \frac{C_{1}^{2} \left(\frac{9}{4} - 6 C_{1}\right)}{4} - \frac{3 C_{1}^{2} \left(4 C_{1} - 1\right)}{16} + \frac{11 C_{1}^{2}}{16} - \frac{C_{1} \left(1 - 8 C_{1}\right)}{128} + \frac{C_{1} \left(3 C_{1} - \frac{5}{8}\right)}{16} + \frac{C_{1} \left(3 C_{1} - \frac{3}{8}\right)}{16} + \frac{3 C_{1} \left(4 C_{1} - 1\right)}{128} + \frac{C_{1} \left(- 6 C_{1}^{2} + \frac{15 C_{1}}{4} - \frac{7}{32}\right)}{4} - \frac{C_{1} \left(96 C_{1}^{2} - 40 C_{1} + 1\right)}{256} - \frac{5 C_{1}}{128} + \frac{1}{1024}\right)}{120 y_{6}^{5}} + O\left(x^{6}\right)$$
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral