Sr Examen
Ecuación diferencial dy*(e^2*y-y)*cosh(x)/dx=2*e^y*x*sinh(x)
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Solución
Ha introducido
[src]
/ 2 \ d y(x)
\-y(x) + e *y(x)/*--(y(x))*cosh(x) = 2*x*e *sinh(x)
dx
$$\left(- y{\left(x \right)} + y{\left(x \right)} e^{2}\right) \cosh{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 2 x e^{y{\left(x \right)}} \sinh{\left(x \right)}$$
(-y + y*exp(2))*cosh(x)*y' = 2*x*exp(y)*sinh(x)
Respuesta
[src]
/ / \
| / | |
| | | 2*x |
| | x | x*e |
2*|- | -------- dx + | -------- dx|
| | 2*x | 2*x |
| | 1 + e | 1 + e |
| | | |
-y(x) \ / / /
(-1 - y(x))*e = C1 + -------------------------------------
(1 + E)*(-1 + E)
$$\left(- y{\left(x \right)} - 1\right) e^{- y{\left(x \right)}} = C_{1} + \frac{2 \left(- \int \frac{x}{e^{2 x} + 1}\, dx + \int \frac{x e^{2 x}}{e^{2 x} + 1}\, dx\right)}{\left(-1 + e\right) \left(1 + e\right)}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st power series
lie group
separable Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 37.815864538043826)
(-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, 3.94276075276142e-62)
(7.777777777777779, 8.388243567336636e+296)
(10.0, 1.33360311798763e+241)
(10.0, 1.33360311798763e+241)