Sr Examen
Ecuación diferencial (9x^2+y−1)dx+(−4y+x)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d d
-1 + 9*x + x*--(y(x)) - 4*--(y(x))*y(x) + y(x) = 0
dx dx
$$9 x^{2} + x \frac{d}{d x} y{\left(x \right)} - 4 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} - 1 = 0$$
9*x^2 + x*y' - 4*y*y' + y - 1 = 0
Respuesta
[src]
_______________________
/ 2 3
\/ C1 + x - 8*x + 24*x x
y(x) = - -------------------------- + -
4 4
$$y{\left(x \right)} = \frac{x}{4} - \frac{\sqrt{C_{1} + 24 x^{3} + x^{2} - 8 x}}{4}$$
_______________________
/ 2 3
x \/ C1 + x - 8*x + 24*x
y(x) = - + --------------------------
4 4
$$y{\left(x \right)} = \frac{x}{4} + \frac{\sqrt{C_{1} + 24 x^{3} + x^{2} - 8 x}}{4}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 26.361402623005052)
(-5.555555555555555, 33.92141731172034)
(-3.333333333333333, 37.19452704421514)
(-1.1111111111111107, 38.424776868036986)
(1.1111111111111107, 39.01912337664415)
(3.333333333333334, 40.252821493066484)
(5.555555555555557, 43.28955337296447)
(7.777777777777779, 48.90151044265769)
(10.0, 57.277391245059405)
(10.0, 57.277391245059405)