In problems below, (a) identify the independent variable and the dependent variable of each equation (use 't' for the independent variable if an independent variable is not given explicitly); (b) give the order of each differential equation (enter '1' for first order, '2' for second order and so on; do not include the quotes); and (c) state whether the equation is linear or nonlinear. if your answer to (c) is nonlinear, make sure that you can explain why this is true.

Our star pitcher, foster enlight, can throw a pitch so fast that it gets to the catcher’s mitt before it leaves foster’s fingers! if the team wins a game then the probability that foster was pitching is 0.8 but only if foster had at least one day’s rest since his last pitching assignment. if foster does not have a day off and the team still wins, the probability that foster was pitching drops by half of what it was on the previous day. if the team wins three games in succession from the toronto tachyons and foster pitched in game #2, what is the probability that he pitched in one or more of the other games? (assume that foster did not pitch on the day before the first game of this three game series.)