Sr Examen
Ecuación diferencial sen(3x)dx+2ycos³(3x)dy=0,
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Solución
Ha introducido
[src]
3 d
2*cos (3*x)*--(y(x))*y(x) + sin(3*x) = 0
dx
$$2 y{\left(x \right)} \cos^{3}{\left(3 x \right)} \frac{d}{d x} y{\left(x \right)} + \sin{\left(3 x \right)} = 0$$
2*y*cos(3*x)^3*y' + sin(3*x) = 0
Respuesta
[src]
___________________
/ 2
-\/ -6 + C1*cos (3*x)
y(x) = ------------------------
6*cos(3*x)
$$y{\left(x \right)} = - \frac{\sqrt{C_{1} \cos^{2}{\left(3 x \right)} - 6}}{6 \cos{\left(3 x \right)}}$$
___________________
/ 2
\/ -6 + C1*cos (3*x)
y(x) = ----------------------
6*cos(3*x)
$$y{\left(x \right)} = \frac{\sqrt{C_{1} \cos^{2}{\left(3 x \right)} - 6}}{6 \cos{\left(3 x \right)}}$$
Gráfico para el problema de Cauchy
Clasificación
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -3.7021312149880816e-09)
(-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, 1.5636038433718505e+185)
(7.777777777777779, 8.38824356733961e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)