Sr Examen
Ecuación diferencial x-sin(x)+sin(y)dx+cos(y)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
x d sin(x) -- + --(y(x))*cos(y(x)) - ------ + sin(y(x)) = 0 dx dx dx
$$\sin{\left(y{\left(x \right)} \right)} + \cos{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + \frac{x}{dx} - \frac{\sin{\left(x \right)}}{dx} = 0$$
sin(y) + cos(y)*y' + x/dx - sin(x)/dx = 0
Respuesta
[src]
/ -x \
|-x + C1*e + sin(x)|
y(x) = pi - asin|--------------------|
\ dx /
$$y{\left(x \right)} = \pi - \operatorname{asin}{\left(\frac{C_{1} e^{- x} - x + \sin{\left(x \right)}}{dx} \right)}$$
/ -x \
|-x + C1*e + sin(x)|
y(x) = asin|--------------------|
\ dx /
$$y{\left(x \right)} = \operatorname{asin}{\left(\frac{C_{1} e^{- x} - x + \sin{\left(x \right)}}{dx} \right)}$$
Clasificación
almost linear
1st power series
lie group
almost linear Integral