Sr Examen
Ecuación diferencial (6xy−2y^2+1)dx+(3x^2-4xy)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 2 d d
1 - 2*y (x) + 3*x *--(y(x)) + 6*x*y(x) - 4*x*--(y(x))*y(x) = 0
dx dx
$$3 x^{2} \frac{d}{d x} y{\left(x \right)} - 4 x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 6 x y{\left(x \right)} - 2 y^{2}{\left(x \right)} + 1 = 0$$
3*x^2*y' - 4*x*y*y' + 6*x*y - 2*y^2 + 1 = 0
Respuesta
[src]
_____________________
/ / 3\
3*x \/ x*\C1 + 8*x + 9*x /
y(x) = --- - ------------------------
4 4*x
$$y{\left(x \right)} = \frac{3 x}{4} - \frac{\sqrt{x \left(C_{1} + 9 x^{3} + 8 x\right)}}{4 x}$$
_____________________
/ / 3\
3*x \/ x*\C1 + 8*x + 9*x /
y(x) = --- + ------------------------
4 4*x
$$y{\left(x \right)} = \frac{3 x}{4} + \frac{\sqrt{x \left(C_{1} + 9 x^{3} + 8 x\right)}}{4 x}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.1718377354408205)
(-5.555555555555555, 2.0158582370093305)
(-3.333333333333333, 3.878676262931692)
(-1.1111111111111107, 9.31590391021562)
(1.1111111111111107, 6999548.024318794)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 1.693402848906264e-52)
(7.777777777777779, 8.388243571809214e+296)
(10.0, 9.036991477623112e-277)
(10.0, 9.036991477623112e-277)