Using the fact that y 1 ( x ) e x is solution of the second order linear homogeneous DE (8 4 x ) y 4 y (4 4 x ) y 0, find a second linearly independent solution y 2 ( x ) using the method of reduction of order (Do NOT enter y 2 ( x ) as part of your answer) and then find the unique solution of the above DE satisfying the initial conditions y (0) 16, y (0) 16

Question: Using the fact that y 1 ( x ) = e x is solution of the second order linear homogeneous DE (8 + 4

Using the fact that y₁(x) = e^x is solution of the second order linear homogeneous DE

(8 + 4x) y′′ − 4 y′ − (4 + 4 x) y = 0,

find a second linearly independent solution y₂(x) using the method of reduction of order (Do NOT enter y₂(x) as part of your answer) and then find the unique solution of the above DE satisfying the initial conditions

y(0) = −16, y′(0) = 16

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