Solve (x-1)dx+ydy=0

$$( x - 1 ) d x + y d y = 0$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=\frac{\sqrt{1-4y^{2}}+1}{2}\text{ or }x=\frac{-\sqrt{1-4y^{2}}+1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply y and y to get y^{2}.

$$\left(x-1\right)dx+y^{2}d=0$$

Use the distributive property to multiply x-1 by d.

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

Use the distributive property to multiply xd-d by x.

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

Combine all terms containing d.

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

Divide 0 by x^{2}-x+y^{2}.

$$d=0$$

Solve for d

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

Steps for Solving Linear Equation

Multiply y and y to get y^{2}.

$$\left(x-1\right)dx+y^{2}d=0$$

Use the distributive property to multiply x-1 by d.

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

Use the distributive property to multiply xd-d by x.

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

Combine all terms containing d.

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

Divide 0 by x^{2}-x+y^{2}.

$$d=0$$

Solve for x (complex solution)

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

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{1-4y^{2}}+1}{2}\text{; }x=\frac{-\sqrt{1-4y^{2}}+1}{2}\text{, }&|y|\leq \frac{1}{2}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$