Sr Examen
Ecuación diferencial sin(y)*(dy/dx)-2cos(y)*cos(x)+cos(x)*sin^2(x)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d
sin (x)*cos(x) + --(y(x))*sin(y(x)) - 2*cos(x)*cos(y(x)) = 0
dx
$$\sin^{2}{\left(x \right)} \cos{\left(x \right)} + \sin{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} - 2 \cos{\left(x \right)} \cos{\left(y{\left(x \right)} \right)} = 0$$
sin(x)^2*cos(x) + sin(y)*y' - 2*cos(x)*cos(y) = 0
Respuesta
[src]
/1 sin(x) cos(2*x) -2*sin(x)\
y(x) = - acos|- - ------ - -------- + C1*e | + 2*pi
\2 2 4 /
$$y{\left(x \right)} = - \operatorname{acos}{\left(C_{1} e^{- 2 \sin{\left(x \right)}} - \frac{\sin{\left(x \right)}}{2} - \frac{\cos{\left(2 x \right)}}{4} + \frac{1}{2} \right)} + 2 \pi$$
/1 sin(x) cos(2*x) -2*sin(x)\
y(x) = acos|- - ------ - -------- + C1*e |
\2 2 4 /
$$y{\left(x \right)} = \operatorname{acos}{\left(C_{1} e^{- 2 \sin{\left(x \right)}} - \frac{\sin{\left(x \right)}}{2} - \frac{\cos{\left(2 x \right)}}{4} + \frac{1}{2} \right)}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
almost linear
1st power series
lie group
1st exact Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -2.097413778449525e-09)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 1.7373559329555976e-47)
(7.777777777777779, 8.388243571809205e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)