Whakaoti i te 3ay^2dy=ay^3+c

$$3 a y ^ { 2 } d y = a y ^ { 3 } + c$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=\frac{c}{\left(3d-1\right)y^{3}}\text{, }&y\neq 0\text{ and }d\neq \frac{1}{3}\\a\in \mathrm{C}\text{, }&\left(y=0\text{ or }d=\frac{1}{3}\right)\text{ and }c=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.

$$3ay^{3}d=ay^{3}+c$$

Tangohia te ay^{3} mai i ngā taha e rua.

$$3ay^{3}d-ay^{3}=c$$

Whakaraupapatia anō ngā kīanga tau.

$$3ady^{3}-ay^{3}=c$$

Pahekotia ngā kīanga tau katoa e whai ana i te a.

$$\left(3dy^{3}-y^{3}\right)a=c$$

Whakawehea ngā taha e rua ki te 3dy^{3}-y^{3}.

$$\frac{\left(3dy^{3}-y^{3}\right)a}{3dy^{3}-y^{3}}=\frac{c}{3dy^{3}-y^{3}}$$

Mā te whakawehe ki te 3dy^{3}-y^{3} ka wetekia te whakareanga ki te 3dy^{3}-y^{3}.

$$a=\frac{c}{3dy^{3}-y^{3}}$$

Whakawehe c ki te 3dy^{3}-y^{3}.

$$a=\frac{c}{\left(3d-1\right)y^{3}}$$

Whakaoti mō a

$$\left\{\begin{matrix}a=\frac{c}{\left(3d-1\right)y^{3}}\text{, }&y\neq 0\text{ and }d\neq \frac{1}{3}\\a\in \mathrm{R}\text{, }&\left(y=0\text{ or }d=\frac{1}{3}\right)\text{ and }c=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.

$$3ay^{3}d=ay^{3}+c$$

Tangohia te ay^{3} mai i ngā taha e rua.

$$3ay^{3}d-ay^{3}=c$$

Whakaraupapatia anō ngā kīanga tau.

$$3ady^{3}-ay^{3}=c$$

Pahekotia ngā kīanga tau katoa e whai ana i te a.

$$\left(3dy^{3}-y^{3}\right)a=c$$

Whakawehea ngā taha e rua ki te 3dy^{3}-y^{3}.

$$\frac{\left(3dy^{3}-y^{3}\right)a}{3dy^{3}-y^{3}}=\frac{c}{3dy^{3}-y^{3}}$$

Mā te whakawehe ki te 3dy^{3}-y^{3} ka wetekia te whakareanga ki te 3dy^{3}-y^{3}.

$$a=\frac{c}{3dy^{3}-y^{3}}$$

Whakawehe c ki te 3dy^{3}-y^{3}.

$$a=\frac{c}{\left(3d-1\right)y^{3}}$$

Whakaoti mō c

$$c=a\left(3d-1\right)y^{3}$$