Sr Examen
Ecuación diferencial xydx+(x^2-y^2+1)dy=0
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Solución
Ha introducido
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2 d 2 d d
x*y(x) + x *--(y(x)) - y (x)*--(y(x)) + --(y(x)) = 0
dx dx dx
$$x^{2} \frac{d}{d x} y{\left(x \right)} + x y{\left(x \right)} - y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y' + x*y - y^2*y' + y' = 0
Respuesta
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/ 2 / 4 2
y(x) = -\/ 1 + x - \/ C1 + x + 2*x
$$y{\left(x \right)} = - \sqrt{x^{2} - \sqrt{C_{1} + x^{4} + 2 x^{2}} + 1}$$
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/ 2 / 4 2
y(x) = \/ 1 + x - \/ C1 + x + 2*x
$$y{\left(x \right)} = \sqrt{x^{2} - \sqrt{C_{1} + x^{4} + 2 x^{2}} + 1}$$
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/ ________________
/ 2 / 4 2
y(x) = -\/ 1 + x + \/ C1 + x + 2*x
$$y{\left(x \right)} = - \sqrt{x^{2} + \sqrt{C_{1} + x^{4} + 2 x^{2}} + 1}$$
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/ 2 / 4 2
y(x) = \/ 1 + x + \/ C1 + x + 2*x
$$y{\left(x \right)} = \sqrt{x^{2} + \sqrt{C_{1} + x^{4} + 2 x^{2}} + 1}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
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(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.9634871678468406)
(-5.555555555555555, 1.3529877612197732)
(-3.333333333333333, 2.51682576379667)
(-1.1111111111111107, 3.2626156986288612)
(1.1111111111111107, 6.902513675931e-310)
(3.333333333333334, 6.902513675931e-310)
(5.555555555555557, 6.9025138568365e-310)
(7.777777777777779, 6.90251463126265e-310)
(10.0, 6.90251463126265e-310)
(10.0, 6.90251463126265e-310)