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