Sr Examen
Ecuación diferencial ln(cos(y))dx+x*tg(y)dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d x*--(y(x))*tan(y(x)) + log(cos(y(x))) = 0 dx
$$x \tan{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + \log{\left(\cos{\left(y{\left(x \right)} \right)} \right)} = 0$$
x*tan(y)*y' + log(cos(y)) = 0
Respuesta
[src]
y(x)
/
|
| tan(y)
| ----------- dy = C1 - log(x)
| log(cos(y))
|
/
$$\int\limits^{y{\left(x \right)}} \frac{\tan{\left(y \right)}}{\log{\left(\cos{\left(y \right)} \right)}}\, dy = C_{1} - \log{\left(x \right)}$$
Gráfico para el problema de Cauchy
Clasificación
separable
1st exact
almost linear
separable reduced
lie group
separable Integral
1st exact Integral
almost linear Integral
separable reduced Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.6692470411943122)
(-5.555555555555555, 0.5722761189431979)
(-3.333333333333333, 0.44848454600814164)
(-1.1111111111111107, 0.2619590763209393)
(1.1111111111111107, -0.13456099512917338)
(3.333333333333334, -0.23236118080970208)
(5.555555555555557, -0.2990682035054363)
(7.777777777777779, -0.3527890425481177)
(10.0, -0.3988106270996335)
(10.0, -0.3988106270996335)