Sr Examen
Ecuación diferencial dx/(x^2-xy+y^2)=dy/(2y^2-xy)
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Solución
Ha introducido
[src]
1 dy ------------------- = ---------------------- 2 2 2 x + y (x) - x*y(x) 2*dx*y (x) - dx*x*y(x)
$$\frac{1}{x^{2} - x y{\left(x \right)} + y^{2}{\left(x \right)}} = \frac{dy}{- dx x y{\left(x \right)} + 2 dx y^{2}{\left(x \right)}}$$
1/(x^2 - x*y + y^2) = dy/(-dx*x*y + 2*dx*y^2)
Respuesta
[src]
/ _______________________\
| / 2 2 |
x*\dx - dy - \/ dx - 3*dy + 6*dx*dy /
y(x) = ----------------------------------------
2*(-dy + 2*dx)
$$y{\left(x \right)} = \frac{x \left(dx - dy - \sqrt{dx^{2} + 6 dx dy - 3 dy^{2}}\right)}{2 \left(2 dx - dy\right)}$$
/ _______________________ \
| / 2 2 |
x*\dx + \/ dx - 3*dy + 6*dx*dy - dy/
y(x) = ----------------------------------------
2*(-dy + 2*dx)
$$y{\left(x \right)} = \frac{x \left(dx - dy + \sqrt{dx^{2} + 6 dx dy - 3 dy^{2}}\right)}{2 \left(2 dx - dy\right)}$$
Clasificación
nth algebraic
nth algebraic Integral