(a) What is the method of variation of parameters based on? (b) Obtain the general solution ofthe non-homogenous equation y"+5y'+6y= 4 by the method of variation of parameters. (c) Determine the generai solutu of the cquation x'y"-2xy'-4y 0 for x>0, using the transformation x e' Question 5 (a) Determine the Laplace transform of the following functions for all t 20 (i) f(t) = Cosat (ii) f) et (b) Find the inverse Laplace transform of F(s) = (iii) f(t) = t S+1 S-6S+18 (c) Solve the Laplace transform of the Differential equation. j+2y+y= F(t), y(0)=j(0)-= 0 Question 6 (a) Define the following (i) ordinary point (ii) Singular point (iii) Irregular singular point (b) Show whether x= 0 is an orcinary point of the equation xy" + 2y' +x= 0 (c) Find the solution of the differential equation (1+x)y"-4.xy'+6y= 0 Using power series method.