Sr Examen
Ecuación diferencial (x+senx+seny)dx+(cosy)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d
x + --(y(x))*cos(y(x)) + sin(x) + sin(y(x)) = 0
dx
$$x + \sin{\left(x \right)} + \sin{\left(y{\left(x \right)} \right)} + \cos{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x + sin(x) + sin(y) + cos(y)*y' = 0
Respuesta
[src]
/ ___ / pi\\
| \/ 2 *cos|x + --||
| -x \ 4 /|
y(x) = pi - asin|1 - x + C1*e + -----------------|
\ 2 /
$$y{\left(x \right)} = \pi - \operatorname{asin}{\left(C_{1} e^{- x} - x + \frac{\sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}}{2} + 1 \right)}$$
/ ___ / pi\\
| \/ 2 *cos|x + --||
| -x \ 4 /|
y(x) = asin|1 - x + C1*e + -----------------|
\ 2 /
$$y{\left(x \right)} = \operatorname{asin}{\left(C_{1} e^{- x} - x + \frac{\sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}}{2} + 1 \right)}$$
Gráfico para el problema de Cauchy
Clasificación
almost linear
1st power series
lie group
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 1.5707964832592054)
(-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, 1.7373559329555976e-47)
(7.777777777777779, 8.388243567719168e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)