I am a first reader of Differential Equation. I was solving a differential equation whose solution is $ |f(x)|= c$ . Now my question is can I write that the solution is $ f(x)= k$ . If $ f(x)$ is continuous then I can remove the mod.
But I am not sure whether the function $ f(x)$ is continuous or not. (Here $ c$ and $ k$ are constants)
So that’s why my question is the following. Is the solution of every differential equation CONTINUOUS in it’s given domain?
Can anyone please help me to understand this?
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