Datrys dy/dydydx=1-1/sqrt{2}

$$\frac { d y } { d y } d y d x = 1 - \frac { 1 } { \sqrt { 2 } }$$

Datrys ar gyfer x

$$x=\frac{\sqrt{2}\left(\sqrt{2}-1\right)}{2yd^{2}}$$

$$d\neq 0\text{ and }y\neq 0$$

Camau ar gyfer Datrys Hafaliad Llinol

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

$$\frac{\mathrm{d}(y)}{\mathrm{d}y}d^{2}yx=1-\frac{1}{\sqrt{2}}$$

Mae'n rhesymoli enwadur \frac{1}{\sqrt{2}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{2}.

$$\frac{\mathrm{d}(y)}{\mathrm{d}y}d^{2}yx=1-\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

Sgwâr \sqrt{2} yw 2.

$$\frac{\mathrm{d}(y)}{\mathrm{d}y}d^{2}yx=1-\frac{\sqrt{2}}{2}$$

Lluoswch ddwy ochr yr hafaliad â 2.

$$2\frac{\mathrm{d}(y)}{\mathrm{d}y}d^{2}yx=2-\sqrt{2}$$

Mae'r hafaliad yn y ffurf safonol.

$$2yd^{2}x=2-\sqrt{2}$$

Rhannu’r ddwy ochr â 2d^{2}y.

$$\frac{2yd^{2}x}{2yd^{2}}=\frac{2-\sqrt{2}}{2yd^{2}}$$

Mae rhannu â 2d^{2}y yn dad-wneud lluosi â 2d^{2}y.

$$x=\frac{2-\sqrt{2}}{2yd^{2}}$$

Datrys ar gyfer d (complex solution)

$$d=-\frac{\sqrt{4-2\sqrt{2}}x^{-\frac{1}{2}}y^{-\frac{1}{2}}}{2}$$

$$d=\frac{\sqrt{4-2\sqrt{2}}x^{-\frac{1}{2}}y^{-\frac{1}{2}}}{2}\text{, }x\neq 0\text{ and }y\neq 0$$

Datrys ar gyfer d

$$d=\frac{\sqrt{\frac{4-2\sqrt{2}}{xy}}}{2}$$

$$d=-\frac{\sqrt{\frac{4-2\sqrt{2}}{xy}}}{2}\text{, }\left(x>0\text{ and }y>0\right)\text{ or }\left(y<0\text{ and }x<0\right)$$