Consider the first order differential equation $y^{\text{'}}+(\frac{x}{x^2-25})y=\frac{e^x}{x-9}$

For each of the initial conditions below, determine the largest interval $y(-7)=1\mathrm{.}7=y(-2\mathrm{.}5)=-5\mathrm{.}5=y(0)=0=y(7\mathrm{.}5)=2\mathrm{.}6=y(10)=-2\mathrm{.}1=aon$ which the existence and uniqueness theorem for first order linear differential equations guarantees the existence $of$ a unique solution.

$(a)y(-7)=1\mathrm{.}7=>$ Interval $=$

$(b)y(-2\mathrm{.}5)=-5\mathrm{.}5=>$ Interval $=$

$(c)y(0)=0=>$ Interval $=$

$(d)y(7\mathrm{.}5)=2\mathrm{.}6=>$ Interval $=$

$(e)y(10)=-2\mathrm{.}1=>$ Interval $=$