Sr Examen
Ecuación diferencial sqrt(3+y*y)*dx-y*dy=(x*x)*y*dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
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/ 2 d 2 d
\/ 3 + y (x) - --(y(x))*y(x) = x *--(y(x))*y(x)
dx dx
$$\sqrt{y^{2}{\left(x \right)} + 3} - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
sqrt(y^2 + 3) - y*y' = x^2*y*y'
Respuesta
[src]
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/ 2 2
y(x) = -\/ -3 + C1 + atan (x) + 2*C1*atan(x)
$$y{\left(x \right)} = - \sqrt{C_{1}^{2} + 2 C_{1} \operatorname{atan}{\left(x \right)} + \operatorname{atan}^{2}{\left(x \right)} - 3}$$
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/ 2 2
y(x) = \/ -3 + C1 + atan (x) + 2*C1*atan(x)
$$y{\left(x \right)} = \sqrt{C_{1}^{2} + 2 C_{1} \operatorname{atan}{\left(x \right)} + \operatorname{atan}^{2}{\left(x \right)} - 3}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st power series
lie group
separable Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.8183842875809667)
(-5.555555555555555, 0.9298902146907535)
(-3.333333333333333, 1.1503337613583793)
(-1.1111111111111107, 1.8312430379637152)
(1.1111111111111107, 3.8224575399488536)
(3.333333333333334, 4.3023666800595315)
(5.555555555555557, 4.424336959691076)
(7.777777777777779, 4.478228285177723)
(10.0, 4.508452255666336)
(10.0, 4.508452255666336)