Sr Examen
Ecuación diferencial ctg(x)cos^2(y)dx=-sin^2(x)tg(y)dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 2 d
cos (y(x))*cot(x) = -sin (x)*--(y(x))*tan(y(x))
dx
$$\cos^{2}{\left(y{\left(x \right)} \right)} \cot{\left(x \right)} = - \sin^{2}{\left(x \right)} \tan{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)}$$
cos(y)^2*cot(x) = -sin(x)^2*tan(y)*y'
Respuesta
[src]
/ ________________ \
| / 1 |
y(x) = - acos|- / -------------- *sin(x)| + 2*pi
| / 2 |
\ \/ 1 + C1*sin (x) /
$$y{\left(x \right)} = - \operatorname{acos}{\left(- \sqrt{\frac{1}{C_{1} \sin^{2}{\left(x \right)} + 1}} \sin{\left(x \right)} \right)} + 2 \pi$$
/ ________________ \
| / 1 |
y(x) = - acos| / -------------- *sin(x)| + 2*pi
| / 2 |
\\/ 1 + C1*sin (x) /
$$y{\left(x \right)} = - \operatorname{acos}{\left(\sqrt{\frac{1}{C_{1} \sin^{2}{\left(x \right)} + 1}} \sin{\left(x \right)} \right)} + 2 \pi$$
/ ________________ \
| / 1 |
y(x) = acos|- / -------------- *sin(x)|
| / 2 |
\ \/ 1 + C1*sin (x) /
$$y{\left(x \right)} = \operatorname{acos}{\left(- \sqrt{\frac{1}{C_{1} \sin^{2}{\left(x \right)} + 1}} \sin{\left(x \right)} \right)}$$
/ ________________ \
| / 1 |
y(x) = acos| / -------------- *sin(x)|
| / 2 |
\\/ 1 + C1*sin (x) /
$$y{\left(x \right)} = \operatorname{acos}{\left(\sqrt{\frac{1}{C_{1} \sin^{2}{\left(x \right)} + 1}} \sin{\left(x \right)} \right)}$$
Gráfico para el problema de Cauchy
Clasificación
separable
lie group
separable Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 3.1415926592729284)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 5.107659831618641e-38)
(7.777777777777779, 8.388243566957436e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)