Sr Examen
Ecuación diferencial sec^2xtgydx+sec^2ytgxdy=0
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Solución
Ha introducido
[src]
2 2 d
sec (x)*tan(y(x)) + sec (y(x))*--(y(x))*tan(x) = 0
dx
$$\tan{\left(x \right)} \sec^{2}{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + \tan{\left(y{\left(x \right)} \right)} \sec^{2}{\left(x \right)} = 0$$
tan(x)*sec(y)^2*y' + tan(y)*sec(x)^2 = 0
Respuesta
[src]
/ 2 2 4*C1\
|1 - cos (x) - cos (x)*e |
acos|---------------------------|
| 2 2 4*C1|
\1 - cos (x) + cos (x)*e /
y(x) = pi - ---------------------------------
2
$$y{\left(x \right)} = \pi - \frac{\operatorname{acos}{\left(\frac{- e^{4 C_{1}} \cos^{2}{\left(x \right)} - \cos^{2}{\left(x \right)} + 1}{e^{4 C_{1}} \cos^{2}{\left(x \right)} - \cos^{2}{\left(x \right)} + 1} \right)}}{2}$$
/ 2 2 4*C1\
|-1 + cos (x) + cos (x)*e |
acos|----------------------------|
| 2 2 4*C1|
\-1 + cos (x) - cos (x)*e /
y(x) = ----------------------------------
2
$$y{\left(x \right)} = \frac{\operatorname{acos}{\left(\frac{e^{4 C_{1}} \cos^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 1}{- e^{4 C_{1}} \cos^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 1} \right)}}{2}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
almost linear
lie group
separable Integral
1st exact Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 2.7282267710197226)
(-5.555555555555555, 3.1415893903810566)
(-3.333333333333333, 3.1416092228172787)
(-1.1111111111111107, 6.283186830127612)
(1.1111111111111107, 9.424776207707366)
(3.333333333333334, 12.566344135993731)
(5.555555555555557, 12.566376318724451)
(7.777777777777779, 15.707962829192384)
(10.0, 18.849546154809968)
(10.0, 18.849546154809968)