# differential equations – Solve ODE transformed into q-difference in Mathematica

Let’s take a simple differential equation:

$$frac{dx}{dt} = -x(t)$$

Suppose we want to do a q-transform. To do this, we will replace the time derivative $$frac{d}{dt}$$ with the q-derivative (also known as the Jackson’s derivative: q-derivative).

$$frac{x(q cdot t) – x(t)}{q cdot t – t} = -x(t)$$

Question: how to solve the resulting equation in Mathematica?