Sr Examen
Ecuación diferencial ydx+(xy+2x-ye^y)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d d d y(x)
2*x*--(y(x)) + x*--(y(x))*y(x) - --(y(x))*e *y(x) + y(x) = 0
dx dx dx
$$x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 x \frac{d}{d x} y{\left(x \right)} - y{\left(x \right)} e^{y{\left(x \right)}} \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} = 0$$
x*y*y' + 2*x*y' - y*exp(y)*y' + y = 0
Respuesta
[src]
/ / 2 \ y(x)\ | 2 \-1 - 2*y (x) + 2*y(x)/*e | y(x) |x*y (x) + -----------------------------|*e = C1 \ 4 /
$$\left(x y^{2}{\left(x \right)} + \frac{\left(- 2 y^{2}{\left(x \right)} + 2 y{\left(x \right)} - 1\right) e^{y{\left(x \right)}}}{4}\right) e^{y{\left(x \right)}} = C_{1}$$
Clasificación
1st exact
1st power series
lie group
1st exact Integral