Question: Question 3 Solve the given differential equation by using Green's function. y - 4y = e 2X, y (0) = 0, y' ( 0 )

Question 3 Solve the given differential equation by using Green's function. y" - 4y = e 2X, y (0) = 0, y' ( 0 ) = 0 Hint: Use the following formula. VI (D Y 2 ( x ) -1 1 ( 1 ) ) 2 (1) G (x, t ) =- W ( t) Y = / G(x, of (1)dt Oy(x) = 1xe 2X_ _ e3x+ 1 e -3x Oy = 1xe 2X- - 3X + + e-4x Oy( = 1xe 2X- Le2X+ Le -2x O y( = 1 xe 2X. 1 e 5x + 1 8-2x

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