Solve 2*xdx=-d(1-x^2)

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

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=i\text{ or }x=-i\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

Multiply -1 and -1 to get 1.

$$2x^{2}d=-d+dx^{2}$$

Add d to both sides.

$$2x^{2}d+d=dx^{2}$$

Subtract dx^{2} from both sides.

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

Combine 2x^{2}d and -dx^{2} to get x^{2}d.

$$x^{2}d+d=0$$

Combine all terms containing d.

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

Divide 0 by x^{2}+1.

$$d=0$$

Solve for d

$$d=0$$

Steps for Solving Linear Equation

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

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

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

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

Multiply -1 and -1 to get 1.

$$2x^{2}d=-d+dx^{2}$$

Add d to both sides.

$$2x^{2}d+d=dx^{2}$$

Subtract dx^{2} from both sides.

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

Combine 2x^{2}d and -dx^{2} to get x^{2}d.

$$x^{2}d+d=0$$

Combine all terms containing d.

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

Divide 0 by x^{2}+1.

$$d=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=i\text{; }x=-i\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Solve for x

$$x\in \mathrm{R}$$

$$d=0$$