Solve y=x-e^-delta*1*xi(omegat)

$$y = x - e ^ { - \delta \cdot 1 } \cdot x i ( \omega t )$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=\frac{\left(x-y\right)e^{\delta }}{\xi \omega }\text{, }&\omega \neq 0\text{ and }\xi \neq 0\\t\in \mathrm{C}\text{, }&y=x\text{ and }\left(\omega =0\text{ or }\xi =0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$x-e^{\left(-\delta \right)\times 1}\xi \omega t=y$$

Reorder the terms.

$$x-t\xi \omega e^{-\delta }=y$$

Subtract x from both sides.

$$-t\xi \omega e^{-\delta }=y-x$$

The equation is in standard form.

$$\left(-\frac{\xi \omega }{e^{\delta }}\right)t=y-x$$

Divide both sides by -\xi \omega e^{-\delta }.

$$\frac{\left(-\frac{\xi \omega }{e^{\delta }}\right)t}{-\frac{\xi \omega }{e^{\delta }}}=\frac{y-x}{-\frac{\xi \omega }{e^{\delta }}}$$

Dividing by -\xi \omega e^{-\delta } undoes the multiplication by -\xi \omega e^{-\delta }.

$$t=\frac{y-x}{-\frac{\xi \omega }{e^{\delta }}}$$

Divide y-x by -\xi \omega e^{-\delta }.

$$t=-\frac{\left(y-x\right)e^{\delta }}{\xi \omega }$$

Solve for t

$$\left\{\begin{matrix}t=\frac{\left(x-y\right)e^{\delta }}{\xi \omega }\text{, }&\omega \neq 0\text{ and }\xi \neq 0\\t\in \mathrm{R}\text{, }&y=x\text{ and }\left(\omega =0\text{ or }\xi =0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$x-e^{\left(-\delta \right)\times 1}\xi \omega t=y$$

Reorder the terms.

$$x-t\xi \omega e^{-\delta }=y$$

Subtract x from both sides.

$$-t\xi \omega e^{-\delta }=y-x$$

The equation is in standard form.

$$\left(-\frac{\xi \omega }{e^{\delta }}\right)t=y-x$$

Divide both sides by -\xi \omega e^{-\delta }.

$$\frac{\left(-\frac{\xi \omega }{e^{\delta }}\right)t}{-\frac{\xi \omega }{e^{\delta }}}=\frac{y-x}{-\frac{\xi \omega }{e^{\delta }}}$$

Dividing by -\xi \omega e^{-\delta } undoes the multiplication by -\xi \omega e^{-\delta }.

$$t=\frac{y-x}{-\frac{\xi \omega }{e^{\delta }}}$$

Divide y-x by -\xi \omega e^{-\delta }.

$$t=-\frac{\left(y-x\right)e^{\delta }}{\xi \omega }$$

Solve for x

$$x=\frac{t\xi \omega }{e^{\delta }}+y$$