What I have tried to do was to separate variables and integrate both sides but what I got was y+ln|y-3|=ln|t-3| + c which is undefined for y=3 and t=3. but I don't understand how to get the range for the solution.
2026-02-22 21:57:36.1771797456
What is the solution to the following Cauchy problem?
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The function $f(t) = \dfrac{1}{t-3}$ has a vertical asymptote at $t=3$ which divides the graph of $f(t)$ into two separate parts. Since the initial condition is at time $t=0$, the solution $y(t)=3$ is defined on the interval $(-\infty,3)$.