Solve (t-x)dt+(t+x)dx=0

$$( t - x ) d t + ( t + x ) d x = 0$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

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

$$\left(td-xd\right)t+\left(t+x\right)dx=0$$

Use the distributive property to multiply td-xd by t.

$$dt^{2}-xdt+\left(t+x\right)dx=0$$

Use the distributive property to multiply t+x by d.

$$dt^{2}-xdt+\left(td+xd\right)x=0$$

Use the distributive property to multiply td+xd by x.

$$dt^{2}-xdt+tdx+dx^{2}=0$$

Combine -xdt and tdx to get 0.

$$dt^{2}+dx^{2}=0$$

Combine all terms containing d.

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

The equation is in standard form.

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

Divide 0 by t^{2}+x^{2}.

$$d=0$$

Solve for d

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

Steps for Solving Linear Equation

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

$$\left(td-xd\right)t+\left(t+x\right)dx=0$$

Use the distributive property to multiply td-xd by t.

$$dt^{2}-xdt+\left(t+x\right)dx=0$$

Use the distributive property to multiply t+x by d.

$$dt^{2}-xdt+\left(td+xd\right)x=0$$

Use the distributive property to multiply td+xd by x.

$$dt^{2}-xdt+tdx+dx^{2}=0$$

Combine -xdt and tdx to get 0.

$$dt^{2}+dx^{2}=0$$

Combine all terms containing d.

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

The equation is in standard form.

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

Divide 0 by t^{2}+x^{2}.

$$d=0$$

Solve for t (complex solution)

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

Solve for t

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