Sr Examen
Ecuación diferencial log(x)sin(y)^3dx-xcos(y)dy=0
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Solución
Ha introducido
[src]
3 d
sin (y(x))*log(x) - x*--(y(x))*cos(y(x)) = 0
dx
$$- x \cos{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + \log{\left(x \right)} \sin^{3}{\left(y{\left(x \right)} \right)} = 0$$
-x*cos(y)*y' + log(x)*sin(y)^3 = 0
Respuesta
[src]
/ ______________\
| / -1 |
y(x) = pi - asin| / ------------ |
| / 2 |
\\/ C1 + log (x) /
$$y{\left(x \right)} = \pi - \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} + \log{\left(x \right)}^{2}}} \right)}$$
/ ______________\
| / -1 |
y(x) = pi + asin| / ------------ |
| / 2 |
\\/ C1 + log (x) /
$$y{\left(x \right)} = \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} + \log{\left(x \right)}^{2}}} \right)} + \pi$$
/ ______________\
| / -1 |
y(x) = -asin| / ------------ |
| / 2 |
\\/ C1 + log (x) /
$$y{\left(x \right)} = - \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} + \log{\left(x \right)}^{2}}} \right)}$$
/ ______________\
| / -1 |
y(x) = asin| / ------------ |
| / 2 |
\\/ C1 + log (x) /
$$y{\left(x \right)} = \operatorname{asin}{\left(\sqrt{- \frac{1}{C_{1} + \log{\left(x \right)}^{2}}} \right)}$$
Clasificación
factorable
separable
lie group
separable Integral