Given a second order o.d.e. a d2y dx2 + b dy dx + c y = f(x) a particular integral is any function, yp(x), which satisfies the equation. That is, any function which when substituted into the left hand side and simplified, results in the function on the right. We denote a particular integral by yp(x). Try each part of this exercise Show that y = −1 4 e2x is a particular integral of d2y dx2 − dy dx − 6y = e2x (1) Part (a) Starting with y = −1 4 e2x, find dy dx and d2y dx2 :