EDB — 1R1

Exercises

1. [1R1]Let \(Θ:ℝ→ℝ\) be a continuous function, Describe all solutions \(f:ℝ→ℝ\) that solve

   \[ ∀ x≠ 0~ ,~ f'(x) = Θ\left(\frac{f(x)}{x}\right) \]

   (Hint: change variables \(f(x) = x h(x)\) and find and solve a differential equation for \(h(x)\).)

   Solution 1

   [1R2]↺↻

   [ [1R3]↺↻]