Sr Examen
Ecuación diferencial y-y'cosx=y^2cosx(1-sinx)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 - --(y(x))*cos(x) + y(x) = y (x)*(1 - sin(x))*cos(x) dx
$$y{\left(x \right)} - \cos{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = \left(1 - \sin{\left(x \right)}\right) y^{2}{\left(x \right)} \cos{\left(x \right)}$$
y - cos(x)*y' = (1 - sin(x))*y^2*cos(x)
Respuesta
[src]
____________
\/ 1 + sin(x)
y(x) = -----------------------------------------------------------
/ / \
| | |
_____________ | | ____________ _____________ |
\/ -1 + sin(x) *|C1 - | \/ 1 + sin(x) *\/ -1 + sin(x) dx|
| | |
\ / /
$$y{\left(x \right)} = \frac{\sqrt{\sin{\left(x \right)} + 1}}{\left(C_{1} - \int \sqrt{\sin{\left(x \right)} - 1} \sqrt{\sin{\left(x \right)} + 1}\, dx\right) \sqrt{\sin{\left(x \right)} - 1}}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
Bernoulli
1st power series
lie group
Bernoulli Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -0.009542698393257956)
(-5.555555555555555, -0.9559628193382362)
(-3.333333333333333, -7617969.126746621)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 2.358677675495031e+184)
(7.777777777777779, 8.388243567716936e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)