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Give the general solution of the second order ODE dy2/d2x - 4dy/dx + 3 = 0

Solving the ansatz equation x^2 - 4x + 3 = gives 2 equal roots where x = 3 and x = 1The general solution therefore is y = Ae^3x + Be^x where A and B are arbitrary constants

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Give the general solution of the second order ODE dy2/d2x - 4dy/dx + 3 = 0

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The infinite series C and S are defined C = acos(x) + a^2cos(2x) + a^3cos(3x) + ..., and S = asin(x) + a^2sin(2x) + a^3sin(3x) + ... where a is a real number and |a| < 1. By considering C+iS, show that S = asin(x)/(1 - 2acos(x) + a^2), and find C.

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Give the general solution of the second order ODE dy2/d2x - 4dy/dx + 3 = 0

Related Further Mathematics A Level answers

Prove ∑r^3 = 1/4 n^2(n+1)^2

Sketch the curve y= ((3x+2)(x-3))/((x-2)(x+1)) and find values of y for which y>=3

The infinite series C and S are defined C = a*cos(x) + a^2*cos(2x) + a^3*cos(3x) + ..., and S = a*sin(x) + a^2*sin(2x) + a^3*sin(3x) + ... where a is a real number and |a| < 1. By considering C+iS, show that S = a*sin(x)/(1 - 2a*cos(x) + a^2), and find C.

Use de Moivre's theorem to calculate an expression for sin(5x) in terms of sin(x) only.

We're here to help

Company Information

Popular Requests

© MyTutorWeb Ltd 2013–2025

CLICK CEOP

The infinite series C and S are defined C = acos(x) + a^2cos(2x) + a^3cos(3x) + ..., and S = asin(x) + a^2sin(2x) + a^3sin(3x) + ... where a is a real number and |a| < 1. By considering C+iS, show that S = asin(x)/(1 - 2acos(x) + a^2), and find C.