ແກ້ dx^2=ydy

$$d x ^ { 2 } = y d y$$

ແກ້ສຳລັບ d (complex solution)

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

ຂັ້ນຕອນສຳລັບການແກ້ສົມຜົນເສັ້ນຊື່

ຄູນ y ກັບ y ເພື່ອໃຫ້ໄດ້ y^{2}.

$$dx^{2}=y^{2}d$$

ລົບ y^{2}d ອອກຈາກທັງສອງຂ້າງ.

$$dx^{2}-y^{2}d=0$$

ຈັດລຳດັບພົດຄືນໃໝ່.

$$dx^{2}-dy^{2}=0$$

ຮວມທຸກຄຳສັບທີ່ມີ d.

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

ຫານ 0 ດ້ວຍ x^{2}-y^{2}.

$$d=0$$

ແກ້ສຳລັບ d

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

ຂັ້ນຕອນສຳລັບການແກ້ສົມຜົນເສັ້ນຊື່

ຄູນ y ກັບ y ເພື່ອໃຫ້ໄດ້ y^{2}.

$$dx^{2}=y^{2}d$$

ລົບ y^{2}d ອອກຈາກທັງສອງຂ້າງ.

$$dx^{2}-y^{2}d=0$$

ຈັດລຳດັບພົດຄືນໃໝ່.

$$dx^{2}-dy^{2}=0$$

ຮວມທຸກຄຳສັບທີ່ມີ d.

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

ຫານ 0 ດ້ວຍ x^{2}-y^{2}.

$$d=0$$

ແກ້ສຳລັບ x (complex solution)

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

ແກ້ສຳລັບ x

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