xy^prime=operatorname{yn}(y/x) eching

$$x y ^ { \prime } = \operatorname { yn } ( \frac { y } { x } )$$

n uchun yechish

$$\left\{\begin{matrix}n=0\text{, }&x\neq 0\\n\in \mathrm{R}\text{, }&y=0\text{ and }x\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x ga ko'paytirish.

$$x\frac{\mathrm{d}}{\mathrm{d}x}(y)x=yny$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(y)=yny$$

y^{2} hosil qilish uchun y va y ni ko'paytirish.

$$x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(y)=y^{2}n$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$y^{2}n=x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Tenglama standart shaklda.

$$y^{2}n=0$$

0 ni y^{2} ga bo'lish.

$$n=0$$

x uchun yechish

$$x\neq 0$$

$$y=0\text{ or }n=0$$