Sr Examen
Ecuación diferencial tgx*sin^2*ydx+cos^2x*ctg*ydy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 2 d
sin (y(x))*tan(x) + cos (x)*--(y(x))*cot(y(x)) = 0
dx
$$\sin^{2}{\left(y{\left(x \right)} \right)} \tan{\left(x \right)} + \cos^{2}{\left(x \right)} \cot{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
sin(y)^2*tan(x) + cos(x)^2*cot(y)*y' = 0
Respuesta
[src]
/ _________________ \
| / -1 |
y(x) = pi - asin| / --------------- *cos(x)|
| / 2 |
\\/ -1 + C1*cos (x) /
$$y{\left(x \right)} = \pi - \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} \cos^{2}{\left(x \right)} - 1}} \cos{\left(x \right)} \right)}$$
/ _________________ \
| / -1 |
y(x) = pi + asin| / --------------- *cos(x)|
| / 2 |
\\/ -1 + C1*cos (x) /
$$y{\left(x \right)} = \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} \cos^{2}{\left(x \right)} - 1}} \cos{\left(x \right)} \right)} + \pi$$
/ _________________ \
| / -1 |
y(x) = -asin| / --------------- *cos(x)|
| / 2 |
\\/ -1 + C1*cos (x) /
$$y{\left(x \right)} = - \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} \cos^{2}{\left(x \right)} - 1}} \cos{\left(x \right)} \right)}$$
/ _________________ \
| / -1 |
y(x) = asin| / --------------- *cos(x)|
| / 2 |
\\/ -1 + C1*cos (x) /
$$y{\left(x \right)} = \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} \cos^{2}{\left(x \right)} - 1}} \cos{\left(x \right)} \right)}$$
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, -0.075998995493158)
(-5.555555555555555, -0.651049662190479)
(-3.333333333333333, 0.7946090654180057)
(-1.1111111111111107, -0.4203911876294279)
(1.1111111111111107, -0.4203912170858424)
(3.333333333333334, 0.7885356717770348)
(5.555555555555557, -0.6486004703368532)
(7.777777777777779, -0.07599514953708092)
(10.0, 0.7080273610098226)
(10.0, 0.7080273610098226)