4. Write down the series expansion of the solution to the Schrödinger equation ut - iuxx = 0 0< x

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Q: Ehe initial value problem: (1 + x²)y" + xy + y = 0, y(0) = 2, y'(0) = –1. 00 8

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Q: 5. Find at least first four non-zero terms in a power series expansion about x = 0 for a general…

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A: Given, x2y''-x1+xy'+y=0 ∴x2y''-x1+xy'+y=0⇒y''-x1+xx2y'+1x2y Therefore Px=-xx+1x2, Qx=1x2…

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Q: 5. Use power series to solve the following differential equation: ax²y" + xy' − y = 0 where a > 0. -

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A: Solution: The equation is xy''+1-xy'-y=0 Since -1=ddx-x+1 Then xy''+1-xy'+ddx-x+1y=0 Add and…

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Q: 2x 1- if 0<x<a/2 Find the Fourier series of f(x)= f(x+7)= f(x). if a/2<x < T

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Q: 3. Obtain series solution of the IVP:  (x+1)y''-(2-x)y' + y=0; y(0)=2, y'(0)=-1

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Q: (b) Verify F(1,1; 2; x) = –x-'ln(1 – x) By expanding each function in a power series about x = 0.

A: The general solution geometrically represents an n-parameter family of curves.

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Q: Q 3. Find the Taylor series of f at the point c for : (a) f(x) = e", c= 2 (c) f(x) = sin x, c= T (b)…

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