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

 

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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 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 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