A function satisfies and

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A function

y

satisfies

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

and

y(-2)=5

. Which pair gives the particular solution and the largest open interval containing

x=-2

on which it is defined? (a)

y=\ln x+5-\ln 2,\;\text{domain }(0,\infty)

(b)

y=\ln|x|+5-\ln 2,\;\text{domain }(-\infty,\infty),\;x\neq0

(c)

y=\ln(-x)+5-\ln 2,\;\text{domain }(-\infty,0)

(d)

y=\ln|x|+5+\ln 2,\;\text{domain }(-\infty,0)