Consider the first order differential equation $y^{\text{'}}+(\frac{x}{x^2-25})y=\frac{e^x}{x-7}.$

For each $of$ the initial conditions below, determine the largest interval $y(-7)=2\mathrm{.}6=y(-3\mathrm{.}5)=6\mathrm{.}4=y(0)=0=y(5\mathrm{.}5)=1\mathrm{.}7=y(10)=2\mathrm{.}6=aon$ which the existence and uniqueness theorem for first order linear differential equations guarantees the

existence $of$ a unique solution.

$(a)y(-7)=2\mathrm{.}6=>$ Interval $=$

$(b)y(-3\mathrm{.}5)=6\mathrm{.}4=>$ Interval $=$

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

$(d)y(5\mathrm{.}5)=1\mathrm{.}7=>$ Interval $=$

$(e)y(10)=2\mathrm{.}6=>$ Interval $=$