Consider the following initial value problem, (4-2)y +5xy-11y = 0, y(0)=0, y'(0) = 2. Note: For...

  

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Consider the following initial value problem, (4-2²)y" +5xy-11y = 0, y(0)=0, y'(0) = 2. 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 = 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.. As part of the solution process you must determine the recurrence relation for the coefficients am. Enter your expression for am+2- am+2= 92 = y(x) = Σ amam m=0 (c) Use your recurrence relation to fill in the blanks below. a3 = a4= B0 am 1. 90. a5 = (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) = a1. POT Consider the following initial value problem, (4-2²)y" +5xy-11y = 0, y(0)=0, y'(0) = 2. 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 = 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.. As part of the solution process you must determine the recurrence relation for the coefficients am. Enter your expression for am+2- am+2= 92 = y(x) = Σ amam m=0 (c) Use your recurrence relation to fill in the blanks below. a3 = a4= B0 am 1. 90. a5 = (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) = a1. POT