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3. a) What is the method of variation of parameters based on? (5marks) b) Using the method of variation of parameters, determine the general

 

3. a) What is the method of variation of parameters based on? (5marks) b) Using the method of variation of parameters, determine the general solution of y'" - 2y' +y = ez,x > 0 c) Determine the general solution of the differential equation (6 marks) %3D x*y" -- 2xy' - 4y 0 for >0 using the transformation x = et (6) %3D marks) UESTION 4 a) Determine the Laplace Transform of the following functions for al t 2 0 f(t) = 1 (2 marks) f(t) 3t (2 marks) i) i) f(t) = cos at (2 marks) b) Define the following i) Wronskian of a function ( 2 marks) i) Linear dependence and independence of a function ( 2 marks) ii) Solve by Laplace transform technique the differential equation (1,0st < + y(t) = 0, t 25 given that y(0)=D0,v(0)=1(7! 1/2

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