Consider the differential equation y$\text{'}\text{'}=$ex$^2/2+$xy$\text{'}$ where y is considered to be a function of x$.$ In this exercise, you will determine whether or not y$=$ex$22+$c is a solution to the differential equation for any constant c$.($a$)$ First substitute the above expression for y into the left side of the differential equation. In other words, compute y$\text{'}\text{'}.($b$)$ Next substitute the above expression for y into the right side of the differential equation. In other words, compute ex$22+$xy$\text{'}.($c$)$ Based on your answers to $($a$)$ and $($b$),$ can we say that y$=$ex$22$ is a solution to the differential equation? Yes No