Participation Assignment $-$ Section $2\mathrm{.}3$

Name

For the linear first$-$order differential equation $\backslash ($ t$($t$+1)\backslash$frac$\{$d x$\}\{$d t$\}+$t x$=1\backslash )$ where $\backslash ($ x$($e$)=1\backslash ),$ answer the following questions$/$perform the following tasks.

$1.$ What is the standard form of this first$-$order linear differential equation?

$2.$ Based on the initial condition, what is the largest $($aka widest$)$ possible interval of definition for the solution to this IVP?

$3.$ What is the $($fully simplified$)$ integrating factor, $\backslash (\backslash$mu $\backslash )?$

$4.$ Solve the IVP as a function of the implied output variable.