Datrys xdx-(5y^4+3)dy=0

$$x d x - ( 5 y ^ { 4 } + 3 ) d y = 0$$

Datrys ar gyfer d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=-\sqrt{5y^{5}+3y}\text{ or }x=\sqrt{5y^{5}+3y}\end{matrix}\right.$$

Camau ar gyfer Datrys Hafaliad Llinol

Lluosi x a x i gael x^{2}.

$$x^{2}d-\left(5y^{4}+3\right)dy=0$$

Defnyddio’r briodwedd ddosbarthu i luosi 5y^{4}+3 â d.

$$x^{2}d-\left(5y^{4}d+3d\right)y=0$$

Defnyddio’r briodwedd ddosbarthu i luosi 5y^{4}d+3d â y.

$$x^{2}d-\left(5dy^{5}+3dy\right)=0$$

I ddod o hyd i wrthwyneb 5dy^{5}+3dy, dewch o hyd i wrthwyneb pob term.

$$x^{2}d-5dy^{5}-3dy=0$$

Cyfuno pob term sy'n cynnwys d.

$$\left(x^{2}-5y^{5}-3y\right)d=0$$

Rhannwch 0 â x^{2}-5y^{5}-3y.

$$d=0$$

Datrys ar gyfer d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y\geq 0\text{ and }|x|=\sqrt{y\left(5y^{4}+3\right)}\end{matrix}\right.$$

Camau ar gyfer Datrys Hafaliad Llinol

Lluosi x a x i gael x^{2}.

$$x^{2}d-\left(5y^{4}+3\right)dy=0$$

Defnyddio’r briodwedd ddosbarthu i luosi 5y^{4}+3 â d.

$$x^{2}d-\left(5y^{4}d+3d\right)y=0$$

Defnyddio’r briodwedd ddosbarthu i luosi 5y^{4}d+3d â y.

$$x^{2}d-\left(5dy^{5}+3dy\right)=0$$

I ddod o hyd i wrthwyneb 5dy^{5}+3dy, dewch o hyd i wrthwyneb pob term.

$$x^{2}d-5dy^{5}-3dy=0$$

Cyfuno pob term sy'n cynnwys d.

$$\left(x^{2}-5y^{5}-3y\right)d=0$$

Rhannwch 0 â x^{2}-5y^{5}-3y.

$$d=0$$

Datrys ar gyfer x (complex solution)

$$\left\{\begin{matrix}\\x=-\sqrt{y\left(5y^{4}+3\right)}\text{; }x=\sqrt{y\left(5y^{4}+3\right)}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Datrys ar gyfer x

$$\left\{\begin{matrix}x=\sqrt{y\left(5y^{4}+3\right)}\text{; }x=-\sqrt{y\left(5y^{4}+3\right)}\text{, }&y\geq 0\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$