Sr Examen
Ecuación diferencial xtgydx=(x^2-2)dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
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d 2 d
x*tan(y(x)) = - 2*--(y(x)) + x *--(y(x))
dx dx
$$x \tan{\left(y{\left(x \right)} \right)} = x^{2} \frac{d}{d x} y{\left(x \right)} - 2 \frac{d}{d x} y{\left(x \right)}$$
x*tan(y) = x^2*y' - 2*y'
Respuesta
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/ _________\
| / 2 |
y(x) = pi - asin\C1*\/ -2 + x /
$$y{\left(x \right)} = \pi - \operatorname{asin}{\left(C_{1} \sqrt{x^{2} - 2} \right)}$$
/ _________\
| / 2 |
y(x) = asin\C1*\/ -2 + x /
$$y{\left(x \right)} = \operatorname{asin}{\left(C_{1} \sqrt{x^{2} - 2} \right)}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral
Respuesta numérica
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(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.5546181139510447)
(-5.555555555555555, 0.37893498911427453)
(-3.333333333333333, 0.20936505193956542)
(-1.1111111111111107, 0.006884158679566092)
(1.1111111111111107, 0.006884084846398348)
(3.333333333333334, 0.0028367095743508436)
(5.555555555555557, 0.005049073167556128)
(7.777777777777779, 0.00718769036299157)
(10.0, 0.009303581610213779)
(10.0, 0.009303581610213779)