Réitigh 1+x^2y+cxy=0

$$1 + x ^ { 2 } y + c x y = 0$$

Réitigh do c.

$$c=\frac{-yx^{2}-1}{xy}$$

$$y\neq 0\text{ and }x\neq 0$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Bain 1 ón dá thaobh. Is ionann rud ar bith a dhealaítear ó nialas agus a shéanadh.

$$x^{2}y+cxy=-1$$

Bain x^{2}y ón dá thaobh.

$$cxy=-1-x^{2}y$$

Athordaigh na téarmaí.

$$cxy=-yx^{2}-1$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$xyc=-yx^{2}-1$$

Roinn an dá thaobh faoi xy.

$$\frac{xyc}{xy}=\frac{-yx^{2}-1}{xy}$$

Má roinntear é faoi xy cuirtear an iolrúchán faoi xy ar ceal.

$$c=\frac{-yx^{2}-1}{xy}$$

Roinn -yx^{2}-1 faoi xy.

$$c=-x-\frac{1}{xy}$$

Réitigh do x. (complex solution)

$$x=\frac{\sqrt{\left(cy\right)^{2}-4y}}{2y}-\frac{c}{2}$$

$$x=-\frac{\sqrt{\left(cy\right)^{2}-4y}}{2y}-\frac{c}{2}\text{, }y\neq 0$$

Réitigh do x.

$$x=\frac{\sqrt{\left(cy\right)^{2}-4y}}{2y}-\frac{c}{2}$$

$$x=-\frac{\sqrt{\left(cy\right)^{2}-4y}}{2y}-\frac{c}{2}\text{, }y\neq 0\text{ and }\left(c=0\text{ or }y\geq \frac{4}{c^{2}}\text{ or }y<0\right)$$