Sr Examen
Ecuación diferencial ydx-4xdy=y^6dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 6 d
- 4*x*--(y(x)) + y(x) = y (x)*--(y(x))
dx dx
$$- 4 x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} = y^{6}{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
-4*x*y' + y = y^6*y'
Respuesta
[src]
4 2 3 5
x 2261*x 9*x 65*x 21735*x / 6\
y(x) = C1 + --- - ------- - ------ + ------ + -------- + O\x /
5 23 11 17 29
C1 8*C1 2*C1 2*C1 8*C1
$$y{\left(x \right)} = \frac{21735 x^{5}}{8 C_{1}^{29}} - \frac{2261 x^{4}}{8 C_{1}^{23}} + \frac{65 x^{3}}{2 C_{1}^{17}} - \frac{9 x^{2}}{2 C_{1}^{11}} + \frac{x}{C_{1}^{5}} + C_{1} + O\left(x^{6}\right)$$
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral