Question

a) Let y be the solution of the equation y ″ − y = 3 e^(2x)...

a)

Let y be the solution of the equation y ″ − y = 3 e^(2x)

satisfying the conditions y ( 0 ) = 2 and y ′ ( 0 ) = 3.

Find the value of the function f ( x ) = ln ⁡ ( y ( x ) − e^x ) at  x = 3.

b)

Let y be the solution of the equation y ″ − 2 y ′ + y = x − 2

satisfying the conditions y ( 0 ) = 0 and y ′ ( 0 ) = 2.

Find the value of the function f ( x ) = y ( x ) − x e^x at  x = 3.

Math   Calculus   
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