Find all distribution solution to the equation
$$\frac{dT}{dx} + aT =0 $$ $a\in \mathbb{R}$.
How can I do these type of problems in distribution theory. I have no idea on how to start. Thanks in advance!
2026-04-07 12:57:19.1775566639
Solve $\frac{dT}{dx} +aT =0$ in distribution
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Consider the derivative of $e^{ax}T$, as the exponential function is a smooth function, this product is defined for distributions.