(c) Justify the statement: If the equation y" + p(x)y' + q(x)y = 0 admits a solution y = x(ex-e-2x), then the point x = 0 cannot be an ordinary point of the equation. (b) Give an example of a second order linear differential equation with polynomial coefficients possessing exactly four singular points such that the points x = +2 are regular singular points and the points x = ±1 are irregular singular points. Justify your example. 3. (a) Show that x = 0 is a regular singular point for the Laguerre equation xy" + (1 − x)y' + 2y = 0, and using the Frobenius method, show that both roots of the indicial equation are equal to zero. Show that the corresponding series for the solution y = a polynomial and find its explicit form. Σanxn is n=0

Use the first table to answer the question? Parts a,b,c and d

Find the measure of AD if BE = 4, BD = 10, and CE = 4.

3 A man filled his car's 8-gallon gas tank. He took a trip and used of the gas. a. Draw an arrow in the figure to the right to show what his gas gauge looked like after the trip. b. How many gallons of gas were used? a. Choose the correct figure below. O A. b. The man used (Type a whole number.) Q gallon(s). B. E 1₁ Q O C. E 'L m 'LL E Q o Ly "I Q