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The linear equation dy/dx = ay + b has the exact solution y = (y₀ + b/a)e^(ax) − b/a. When a is negative the exponential decays and y approaches the steady state −b/a.
Linear ODE solution
y(x) = (y₀ + b/a)·e^(ax) − b/a, for a ≠ 0
The steady state is 4, and y(4) = (1 − 4)e⁻² + 4 ≈ 3.5939942.
It is the value where dy/dx = 0, so the system stops changing — stable when a is negative.