Consider the following initial value problem, (4-x²)y" +7xy' - 27y= 0, y(0) = 0, y'(0) = 6. Note: For each part below yo

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Consider The Following Initial Value Problem 4 X Y 7xy 27y 0 Y 0 0 Y 0 6 Note For Each Part Below Yo 1 (45.61 KiB) Viewed 40 times

Consider the following initial value problem, (4-x²)y" +7xy' - 27y= 0, y(0) = 0, y'(0) = 6. Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals. (a) This differential equation has singular points at x= 2;-2 Note: You must use a semicolon here to separate your answers. (b) Since there is no singular point at x = 0, you can find a normal power series solution for y(x) about x = 0, i.e., y(x) = Σ amam m=0 As part of the solution process you must determine the recurrence relation for the coefficients am. Enter your expression for am+2 am+2 am (c) Use your recurrence relation to fill in the blanks below. a2 = a0₁ a3= a1. a4= a0₁ = a5= a1. (d) Using your results above and the initial conditions, enter the first three non-zero terms of the power series solution for y(x). y(x) = || 47