Solve (y^2-1)*dx=(x-1)*y*dy

$$( y ^ { 2 } - 1 ) \cdot d x = ( x - 1 ) \cdot y \cdot d y$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=y^{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply y^{2}-1 by d.

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

Use the distributive property to multiply y^{2}d-d by x.

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

Use the distributive property to multiply x-1 by y^{2}.

$$y^{2}dx-dx=\left(xy^{2}-y^{2}\right)d$$

Use the distributive property to multiply xy^{2}-y^{2} by d.

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

Subtract xy^{2}d from both sides.

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

Combine y^{2}dx and -xy^{2}d to get 0.

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

Add y^{2}d to both sides.

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

Combine all terms containing d.

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

The equation is in standard form.

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

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

$$d=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=y^{2}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply y^{2}-1 by d.

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

Use the distributive property to multiply y^{2}d-d by x.

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

Use the distributive property to multiply x-1 by y^{2}.

$$y^{2}dx-dx=\left(xy^{2}-y^{2}\right)d$$

Use the distributive property to multiply xy^{2}-y^{2} by d.

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

Subtract xy^{2}d from both sides.

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

Combine y^{2}dx and -xy^{2}d to get 0.

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

Cancel out -1 on both sides.

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

The equation is in standard form.

$$dx=dy^{2}$$

Divide both sides by d.

$$\frac{dx}{d}=\frac{dy^{2}}{d}$$

Dividing by d undoes the multiplication by d.

$$x=\frac{dy^{2}}{d}$$

Divide y^{2}d by d.

$$x=y^{2}$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=y^{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply y^{2}-1 by d.

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

Use the distributive property to multiply y^{2}d-d by x.

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

Use the distributive property to multiply x-1 by y^{2}.

$$y^{2}dx-dx=\left(xy^{2}-y^{2}\right)d$$

Use the distributive property to multiply xy^{2}-y^{2} by d.

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

Subtract xy^{2}d from both sides.

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

Combine y^{2}dx and -xy^{2}d to get 0.

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

Add y^{2}d to both sides.

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

Combine all terms containing d.

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

The equation is in standard form.

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

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

$$d=0$$

Solve for x

$$\left\{\begin{matrix}\\x=y^{2}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply y^{2}-1 by d.

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

Use the distributive property to multiply y^{2}d-d by x.

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

Use the distributive property to multiply x-1 by y^{2}.

$$y^{2}dx-dx=\left(xy^{2}-y^{2}\right)d$$

Use the distributive property to multiply xy^{2}-y^{2} by d.

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

Subtract xy^{2}d from both sides.

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

Combine y^{2}dx and -xy^{2}d to get 0.

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

Cancel out -1 on both sides.

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

The equation is in standard form.

$$dx=dy^{2}$$

Divide both sides by d.

$$\frac{dx}{d}=\frac{dy^{2}}{d}$$

Dividing by d undoes the multiplication by d.

$$x=\frac{dy^{2}}{d}$$

Divide y^{2}d by d.

$$x=y^{2}$$