Sr Examen
Ecuación diferencial cos^2ydx-tgxdy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d
cos (y(x)) - --(y(x))*tan(x) = 0
dx
$$\cos^{2}{\left(y{\left(x \right)} \right)} - \tan{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
cos(y)^2 - tan(x)*y' = 0
Respuesta
[src]
/ ___________________________________________\
| / 2 2 |
|-1 + \/ 1 + C1 + log (sin(x)) + 2*C1*log(sin(x)) |
y(x) = 2*atan|---------------------------------------------------|
\ C1 + log(sin(x)) /
$$y{\left(x \right)} = 2 \operatorname{atan}{\left(\frac{\sqrt{C_{1}^{2} + 2 C_{1} \log{\left(\sin{\left(x \right)} \right)} + \log{\left(\sin{\left(x \right)} \right)}^{2} + 1} - 1}{C_{1} + \log{\left(\sin{\left(x \right)} \right)}} \right)}$$
/ ___________________________________________\
| / 2 2 |
|1 + \/ 1 + C1 + log (sin(x)) + 2*C1*log(sin(x)) |
y(x) = -2*atan|--------------------------------------------------|
\ C1 + log(sin(x)) /
$$y{\left(x \right)} = - 2 \operatorname{atan}{\left(\frac{\sqrt{C_{1}^{2} + 2 C_{1} \log{\left(\sin{\left(x \right)} \right)} + \log{\left(\sin{\left(x \right)} \right)}^{2} + 1} + 1}{C_{1} + \log{\left(\sin{\left(x \right)} \right)}} \right)}$$
Clasificación
factorable
separable
lie group
separable Integral