(c)Given that y=x is a solution of the differential equation 4x'y-4xy+43= 0 Find a second linearly...

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(c)Given that y=x is a solution of the differential equation 4x'y-4xy+43= 0 Find a second linearly independent solution by the method of reduction of order in the interval x > 0 Question 2 (a) Define the following citing appropriate examples (i) Linearly independent solution (ii) The Wronskian of two ninctions 9 A non homogencus equation of second order. (b) Determine whether the set (6) (1-x, 1+x, 1-3 x} is linearly independent on (-cc, 0) (c) Given the problem y"-4y 0, 0) = 1, y'(0) = 0 verify that y, (x) = cosh 2x and y2 (x) = Sinh 2 x are solutions of the (i) Differential equation show that their Wronskian is not zero (i) (iii) Write the general solution (iv} Find the solution of the initial value problem. Question 3 (e) Giver: the initial value problem y"+Sy+4 = 0, 1(0) =-1, y'(0)=-7 Find () a unique particular solution (ii) the general solution fb) Find the generai sclation of cach equation. my+4y-Sy-0. (c)Given that y=x is a solution of the differential equation 4x'y-4xy+43= 0 Find a second linearly independent solution by the method of reduction of order in the interval x > 0 Question 2 (a) Define the following citing appropriate examples (i) Linearly independent solution (ii) The Wronskian of two ninctions 9 A non homogencus equation of second order. (b) Determine whether the set (6) (1-x, 1+x, 1-3 x} is linearly independent on (-cc, 0) (c) Given the problem y"-4y 0, 0) = 1, y'(0) = 0 verify that y, (x) = cosh 2x and y2 (x) = Sinh 2 x are solutions of the (i) Differential equation show that their Wronskian is not zero (i) (iii) Write the general solution (iv} Find the solution of the initial value problem. Question 3 (e) Giver: the initial value problem y"+Sy+4 = 0, 1(0) =-1, y'(0)=-7 Find () a unique particular solution (ii) the general solution fb) Find the generai sclation of cach equation. my+4y-Sy-0.

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