Sr Examen
Ecuación diferencial expˆ(2*x)*sinˆ3*y+y'(1+expˆ(4*x))*cos*y=0
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Solución
Ha introducido
[src]
3 2*x / 4*x\ d
sin (y(x))*e + \1 + e /*--(y(x))*cos(y(x)) = 0
dx
$$\left(e^{4 x} + 1\right) \cos{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + e^{2 x} \sin^{3}{\left(y{\left(x \right)} \right)} = 0$$
(exp(4*x) + 1)*cos(y)*y' + exp(2*x)*sin(y)^3 = 0
Respuesta
[src]
/ ________________________________\
| / -1 |
y(x) = pi - asin| / ------------------------------ |
| / / x \ |
| / | 1 e | |
| / C1 + atan|-------- - --------| |
| / | 2*x x -x| |
\\/ \1 + e e + e / /
$$y{\left(x \right)} = \pi - \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} + \operatorname{atan}{\left(\frac{1}{e^{2 x} + 1} - \frac{e^{x}}{e^{x} + e^{- x}} \right)}}} \right)}$$
/ ________________________________\
| / -1 |
y(x) = pi + asin| / ------------------------------ |
| / / x \ |
| / | 1 e | |
| / C1 + atan|-------- - --------| |
| / | 2*x x -x| |
\\/ \1 + e e + e / /
$$y{\left(x \right)} = \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} + \operatorname{atan}{\left(\frac{1}{e^{2 x} + 1} - \frac{e^{x}}{e^{x} + e^{- x}} \right)}}} \right)} + \pi$$
/ ________________________________\
| / -1 |
y(x) = -asin| / ------------------------------ |
| / / x \ |
| / | 1 e | |
| / C1 + atan|-------- - --------| |
| / | 2*x x -x| |
\\/ \1 + e e + e / /
$$y{\left(x \right)} = - \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} + \operatorname{atan}{\left(\frac{1}{e^{2 x} + 1} - \frac{e^{x}}{e^{x} + e^{- x}} \right)}}} \right)}$$
/ ________________________________\
| / -1 |
y(x) = asin| / ------------------------------ |
| / / x \ |
| / | 1 e | |
| / C1 + atan|-------- - --------| |
| / | 2*x x -x| |
\\/ \1 + e e + e / /
$$y{\left(x \right)} = \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} + \operatorname{atan}{\left(\frac{1}{e^{2 x} + 1} - \frac{e^{x}}{e^{x} + e^{- x}} \right)}}} \right)}$$
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, 0.7499999506629834)
(-5.555555555555555, 0.7499966215571378)
(-3.333333333333333, 0.7497242990802707)
(-1.1111111111111107, 0.7277104048354252)
(1.1111111111111107, 0.553825524794778)
(3.333333333333334, 0.5449234817899903)
(5.555555555555557, 0.5448210764329197)
(7.777777777777779, 0.5448198686340818)
(10.0, 0.544819853588975)
(10.0, 0.544819853588975)