Sr Examen
Ecuación diferencial (cos(x-2y)+cos(x+2y))*y'=1/cosx^2
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 1
(cos(x - 2*y(x)) + cos(x + 2*y(x)))*--(y(x)) = -------
dx 2
cos (x)
$$\left(\cos{\left(x - 2 y{\left(x \right)} \right)} + \cos{\left(x + 2 y{\left(x \right)} \right)}\right) \frac{d}{d x} y{\left(x \right)} = \frac{1}{\cos^{2}{\left(x \right)}}$$
(cos(x - 2*y) + cos(x + 2*y))*y' = cos(x)^(-2)
Respuesta
[src]
/ log(-1 + sin(x)) log(1 + sin(x)) sin(x) \
asin|C1 - ---------------- + --------------- + ---------|
| 4 4 2 |
pi \ 2*cos (x)/
y(x) = -- - ---------------------------------------------------------
2 2
$$y{\left(x \right)} = - \frac{\operatorname{asin}{\left(C_{1} - \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4} + \frac{\sin{\left(x \right)}}{2 \cos^{2}{\left(x \right)}} \right)}}{2} + \frac{\pi}{2}$$
/ log(-1 + sin(x)) log(1 + sin(x)) sin(x) \
asin|C1 - ---------------- + --------------- + ---------|
| 4 4 2 |
\ 2*cos (x)/
y(x) = ---------------------------------------------------------
2
$$y{\left(x \right)} = \frac{\operatorname{asin}{\left(C_{1} - \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4} + \frac{\sin{\left(x \right)}}{2 \cos^{2}{\left(x \right)}} \right)}}{2}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -0.785398163447232)
(-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, 4.3149409499051355e-61)
(7.777777777777779, 8.388243571810696e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)