Sr Examen
Ecuación diferencial dx*(3*x^2+2*x*y^2)+dy*(2*x^2*y+4*y^3)=0
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Solución
Ha introducido
[src]
2 2 3 d 2 d
3*x + 2*x*y (x) + 4*y (x)*--(y(x)) + 2*x *--(y(x))*y(x) = 0
dx dx
$$2 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 3 x^{2} + 2 x y^{2}{\left(x \right)} + 4 y^{3}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
2*x^2*y*y' + 3*x^2 + 2*x*y^2 + 4*y^3*y' = 0
Respuesta
[src]
____________________________
/ ________________
___ / 2 / 4 3
-\/ 2 *\/ - x - \/ C1 + x - 4*x
y(x) = ----------------------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{2} \sqrt{- x^{2} - \sqrt{C_{1} + x^{4} - 4 x^{3}}}}{2}$$
____________________________
/ ________________
___ / 2 / 4 3
\/ 2 *\/ - x - \/ C1 + x - 4*x
y(x) = --------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt{2} \sqrt{- x^{2} - \sqrt{C_{1} + x^{4} - 4 x^{3}}}}{2}$$
__________________________
/ ________________
___ / / 4 3 2
-\/ 2 *\/ \/ C1 + x - 4*x - x
y(x) = --------------------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{2} \sqrt{- x^{2} + \sqrt{C_{1} + x^{4} - 4 x^{3}}}}{2}$$
__________________________
/ ________________
___ / / 4 3 2
\/ 2 *\/ \/ C1 + x - 4*x - x
y(x) = ------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt{2} \sqrt{- x^{2} + \sqrt{C_{1} + x^{4} - 4 x^{3}}}}{2}$$
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, 9.910226370370948e-10)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 9.836995015458208e-72)
(7.777777777777779, 8.3882435669738e+296)
(10.0, 9.036991477623112e-277)
(10.0, 9.036991477623112e-277)