Sr Examen
Ecuación diferencial sec^2xsecy=y'(ctgx)(siny)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d
sec (x)*sec(y(x)) = --(y(x))*cot(x)*sin(y(x))
dx
$$\sec^{2}{\left(x \right)} \sec{\left(y{\left(x \right)} \right)} = \sin{\left(y{\left(x \right)} \right)} \cot{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
sec(x)^2*sec(y) = sin(y)*cot(x)*y'
Respuesta
[src]
/ ________________\
| / 2 |
|\/ 1 + C1*cos (x) |
y(x) = pi - asin|-------------------|
\ cos(x) /
$$y{\left(x \right)} = \pi - \operatorname{asin}{\left(\frac{\sqrt{C_{1} \cos^{2}{\left(x \right)} + 1}}{\cos{\left(x \right)}} \right)}$$
/ ________________\
| / 2 |
|\/ 1 + C1*cos (x) |
y(x) = pi + asin|-------------------|
\ cos(x) /
$$y{\left(x \right)} = \operatorname{asin}{\left(\frac{\sqrt{C_{1} \cos^{2}{\left(x \right)} + 1}}{\cos{\left(x \right)}} \right)} + \pi$$
/ ________________\
| / 2 |
|\/ 1 + C1*cos (x) |
y(x) = -asin|-------------------|
\ cos(x) /
$$y{\left(x \right)} = - \operatorname{asin}{\left(\frac{\sqrt{C_{1} \cos^{2}{\left(x \right)} + 1}}{\cos{\left(x \right)}} \right)}$$
/ ________________\
| / 2 |
|\/ 1 + C1*cos (x) |
y(x) = asin|-------------------|
\ cos(x) /
$$y{\left(x \right)} = \operatorname{asin}{\left(\frac{\sqrt{C_{1} \cos^{2}{\left(x \right)} + 1}}{\cos{\left(x \right)}} \right)}$$
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, 1.5707963455562954)
(-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, 2.957741787671986e-32)
(7.777777777777779, 8.388243567720354e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)