Sr Examen
Ecuación diferencial ydx-2xdy=2y^4dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 4 d
- 2*x*--(y(x)) + y(x) = 2*y (x)*--(y(x))
dx dx
$$- 2 x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} = 2 y^{4}{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
-2*x*y' + y = 2*y^4*y'
Respuesta
[src]
4 2 3 5
x 429*x 5*x 21*x 2431*x / 6\
y(x) = C1 + ----- - -------- - ----- + ------- + -------- + O\x /
3 15 7 11 19
2*C1 128*C1 8*C1 16*C1 256*C1
$$y{\left(x \right)} = \frac{2431 x^{5}}{256 C_{1}^{19}} - \frac{429 x^{4}}{128 C_{1}^{15}} + \frac{21 x^{3}}{16 C_{1}^{11}} - \frac{5 x^{2}}{8 C_{1}^{7}} + \frac{x}{2 C_{1}^{3}} + C_{1} + O\left(x^{6}\right)$$
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral