TITLE: How many solutions does the following initial value problem have?
QUESTION [0 upvotes]: How many solutions does the following initial value problem have? Explain why.
$tx'+x=1$ , and initial value is $x(0)=0$
The problem is that at $(0,0)$ the function is not continuous, but there exists only one solution.

REPLY [1 votes]: It has none. Assume there is a solution x(t). then $1=0\cdot x'(0)+x(0)=0+0=0$.
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