Réitigh (x^2+y^2)dx=2x^2dy

$$( x ^ { 2 } + y ^ { 2 } ) d x = 2 x ^ { 2 } d y$$

Réitigh do d. (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=y\text{ or }x=0\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun x^{2}+y^{2} a mhéadú faoi d.

$$\left(x^{2}d+y^{2}d\right)x=2x^{2}dy$$

Úsáid an t-airí dáileach chun x^{2}d+y^{2}d a mhéadú faoi x.

$$dx^{3}+y^{2}dx=2x^{2}dy$$

Bain 2x^{2}dy ón dá thaobh.

$$dx^{3}+y^{2}dx-2x^{2}dy=0$$

Comhcheangail na téarmaí ar fad ina bhfuil d.

$$\left(x^{3}+y^{2}x-2x^{2}y\right)d=0$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(x^{3}+xy^{2}-2yx^{2}\right)d=0$$

Roinn 0 faoi x^{3}+y^{2}x-2x^{2}y.

$$d=0$$

Réitigh do d.

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=y\text{ or }x=0\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun x^{2}+y^{2} a mhéadú faoi d.

$$\left(x^{2}d+y^{2}d\right)x=2x^{2}dy$$

Úsáid an t-airí dáileach chun x^{2}d+y^{2}d a mhéadú faoi x.

$$dx^{3}+y^{2}dx=2x^{2}dy$$

Bain 2x^{2}dy ón dá thaobh.

$$dx^{3}+y^{2}dx-2x^{2}dy=0$$

Comhcheangail na téarmaí ar fad ina bhfuil d.

$$\left(x^{3}+y^{2}x-2x^{2}y\right)d=0$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(x^{3}+xy^{2}-2yx^{2}\right)d=0$$

Roinn 0 faoi x^{3}+y^{2}x-2x^{2}y.

$$d=0$$

Réitigh do x. (complex solution)

$$\left\{\begin{matrix}\\x=y\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Réitigh do x.

$$\left\{\begin{matrix}\\x=y\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$