I am solving a differential equation .
I got the solution , a constant.
But the handout by my professor says
"The solution is , a constant. where . But it does not mean that is not defined at . It means that y can take any value at as long as it satisfies ."
It does not make much sense to me because if satisfies the equation at , then the solution will be just , a constant.
And I believe my solution indeed makes sense because , a constant is defined on and differentiable, for any . On the other hand, plugging this in to gives me for any .
Would you explain what the handout is saying?