Consider The Following Initial Value Problem 1 X Y 11xy 38y 0 Y 0 3 Y 0 0 Note For Each Part Below 1 (53.32 KiB) Viewed 37 times
Consider The Following Initial Value Problem 1 X Y 11xy 38y 0 Y 0 3 Y 0 0 Note For Each Part Below 2 (13.9 KiB) Viewed 37 times
Consider the following initial value problem, (1-x²)y" +11xy' - 38y = 0, y(0) = 3, y'(0) = 0. 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., ∞ 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+2₁ am+2 = sam (c) Use your recurrence relation to fill in the blanks below. 92 = ao a3 = a4 a1 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) =
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