Lutasin ang 2(y+x)dx=xy+y

$$2 ( y + x ) d x = x y + y$$

I-solve ang d (complex solution)

$$\left\{\begin{matrix}d=\frac{y\left(x+1\right)}{2x\left(x+y\right)}\text{, }&x\neq 0\text{ and }y\neq -x\\d\in \mathrm{C}\text{, }&\left(y=0\text{ and }x=0\right)\text{ or }\left(x=-1\text{ and }y=1\right)\end{matrix}\right.$$

Mga Hakbang sa Pagso-solve ng Linear Equation

Gamitin ang distributive property para i-multiply ang 2 gamit ang y+x.

$$\left(2y+2x\right)dx=xy+y$$

Gamitin ang distributive property para i-multiply ang 2y+2x gamit ang d.

$$\left(2yd+2xd\right)x=xy+y$$

Gamitin ang distributive property para i-multiply ang 2yd+2xd gamit ang x.

$$2ydx+2dx^{2}=xy+y$$

Pagsamahin ang lahat ng term na naglalaman ng d.

$$\left(2yx+2x^{2}\right)d=xy+y$$

Ang equation ay nasa standard form.

$$\left(2x^{2}+2xy\right)d=xy+y$$

I-divide ang magkabilang dulo ng equation gamit ang 2x^{2}+2xy.

$$\frac{\left(2x^{2}+2xy\right)d}{2x^{2}+2xy}=\frac{xy+y}{2x^{2}+2xy}$$

Kapag na-divide gamit ang 2x^{2}+2xy, ma-a-undo ang multiplication gamit ang 2x^{2}+2xy.

$$d=\frac{xy+y}{2x^{2}+2xy}$$

I-divide ang yx+y gamit ang 2x^{2}+2xy.

$$d=\frac{y\left(x+1\right)}{2x\left(x+y\right)}$$

I-solve ang d

$$\left\{\begin{matrix}d=\frac{y\left(x+1\right)}{2x\left(x+y\right)}\text{, }&x\neq 0\text{ and }y\neq -x\\d\in \mathrm{R}\text{, }&\left(y=0\text{ and }x=0\right)\text{ or }\left(x=-1\text{ and }y=1\right)\end{matrix}\right.$$

Mga Hakbang sa Pagso-solve ng Linear Equation

Gamitin ang distributive property para i-multiply ang 2 gamit ang y+x.

$$\left(2y+2x\right)dx=xy+y$$

Gamitin ang distributive property para i-multiply ang 2y+2x gamit ang d.

$$\left(2yd+2xd\right)x=xy+y$$

Gamitin ang distributive property para i-multiply ang 2yd+2xd gamit ang x.

$$2ydx+2dx^{2}=xy+y$$

Pagsamahin ang lahat ng term na naglalaman ng d.

$$\left(2yx+2x^{2}\right)d=xy+y$$

Ang equation ay nasa standard form.

$$\left(2x^{2}+2xy\right)d=xy+y$$

I-divide ang magkabilang dulo ng equation gamit ang 2x^{2}+2xy.

$$\frac{\left(2x^{2}+2xy\right)d}{2x^{2}+2xy}=\frac{xy+y}{2x^{2}+2xy}$$

Kapag na-divide gamit ang 2x^{2}+2xy, ma-a-undo ang multiplication gamit ang 2x^{2}+2xy.

$$d=\frac{xy+y}{2x^{2}+2xy}$$

I-divide ang yx+y gamit ang 2x^{2}+2xy.

$$d=\frac{y\left(x+1\right)}{2x\left(x+y\right)}$$

I-solve ang x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{y\left(y\left(2d-1\right)^{2}+8d\right)}-2dy+y}{4d}\text{; }x=\frac{-\sqrt{y\left(y\left(2d-1\right)^{2}+8d\right)}-2dy+y}{4d}\text{, }&d\neq 0\\x=-1\text{, }&y\neq 0\text{ and }d=0\\x\in \mathrm{C}\text{, }&d=0\text{ and }y=0\end{matrix}\right.$$

I-solve ang x

$$\left\{\begin{matrix}x=\frac{\sqrt{y\left(4yd^{2}-4dy+y+8d\right)}-2dy+y}{4d}\text{; }x=\frac{-\sqrt{y\left(4yd^{2}-4dy+y+8d\right)}-2dy+y}{4d}\text{, }&\left(d\neq 0\text{ and }d\neq \frac{1}{2}\text{ and }y=-\frac{8d}{4d^{2}-4d+1}\right)\text{ or }\left(d\neq 0\text{ and }d\neq \frac{1}{2}\text{ and }y\leq -\frac{8d}{4d^{2}-4d+1}\text{ and }y\leq 0\right)\text{ or }\left(d\neq 0\text{ and }y\geq 0\text{ and }y\geq -\frac{8d}{4d^{2}-4d+1}\right)\text{ or }\left(d=\frac{1}{2}\text{ and }y\geq 0\right)\text{ or }\left(d\neq 0\text{ and }y=0\right)\\x=-1\text{, }&y\neq 0\text{ and }d=0\\x\in \mathrm{R}\text{, }&d=0\text{ and }y=0\end{matrix}\right.$$