5. The differential equation y 00 − xy = 0 is called Airy’s equation, and is used in physics to model the refraction of light. (
a) Assume a power series solution, and find the recurrence relation of the coefficients. [Hint: When shifting the indices, one way is to let m = n − 3, then factor out x n+1 and find an+3 in terms of an. Alternatively, you can find an+2 in terms of an−1.] (b) Show that a2 = 0. [Hint: the two series for y 00 and xy don’t “start” at the same power of x, but for any solution, each term must be zero. (Why?)] (c) Find the particular solution when y(0) = 1, y 0 (0) = 0, as well as the particular solution when y(0) = 0, y 0 (0) = 1.
If I am making a ratio of the tickets Cindy sold to the number of tickets sold in all it would be 40:68 but I would have to simplify and 40 divided by 2 = 20 and 68 divided by 2 = 34 then I would divide them both by two again to get our answer of 10:17! Hope this helps! Have a great day!
Draw a horizontal line from the top corner of the left wall to the right wall. Now you have a rectangle on the bottom 8’x10’ (80 square feet) and a triangle on the top with a height of 5’ and a base of 8’. 1/2 base times height =20. You need to paint 100 sq feet so you need 2 gallons.
