A function satisfies for and the point lies on its graph.

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A function

y

satisfies

\dfrac{dy}{dx}=\dfrac{1}{x-3}

for

x\neq 3

and the point

(1,2)

lies on its graph. (1) Determine the explicit formula for

y(x)

. (2) State the largest open interval containing

x=1

on which this particular solution is valid.