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b. Find the tailor series expansion for about
compute b. Find the tailor series expansion for about "A(1+ 2r) dr 0
1. Find the first three nonzero terms in a power series expansion about Xo = 0 of the general solution of the differential equation y" + (x - 1)y = 0. Hint: Compute up to 04.
1. Find the first three nonzero terms in a power series expansion about Xo = 0 of the general solution of the differential equation y" + (x - 1)y = 0. Hint: Compute up to 01.
2. Find the first three nonzero terms in a power series expansion about to = 0 of the solution of the initial value problem y" - xy + 2y = 0, y(0) = 0,7'0) = 1. Hint: Compute up to 25.
3. Find the first three nonzero terms in a power series expansion about to 1 of the general solution of the differential equation xy + y = 0. Hint: Compute up to a2.
4. Find the first three nonzero terms in a power series expansion about xo = 0 of the general solution of the differential equation y' - y=e". Hint: Compute up to 25.
(C)!!!!! 5. Find the Laurent series expansion of: 1 (a) f(x) = 1 about i, (b) f(x) = 22 + atz, convergent on {2< 121 < 4}, (c)* f(x) = 273-33+2, convergent on {{ < \z – 11 <1}.
Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equation. W -3x?w'+w=0
a) Find the half-range cosine series expansion of the function (1, 0< < f (ar) (. - عام .ج م ہے b) Plot the function F(2) to which the cosine series is convergent.
question 5c 5. Find the Laurent series expansion of: (a) f(x) = 2*1 about i, (b) f(x) = 22 + 1-2, convergent on {2 < 121 <4}, (c)* f(x) = 2,2-33+2, convergent on {j < lz - 11 < 1}.
1. Write the forms of the series expansion about the regular singular point x=0 for two linearly independent solutions to the following differential equation (do not compute the coefficients in the expansions): zºy'(x) - xy'(x) + (1 - x)y(x) = 0. (1) 2. Does the following system of equations have an unique solution? Explain your reason for the answer (do not find the solution). 2x 1 + 4x2 + x3 = 8 2x + 4.62 = 6 -401 - 8x2...