Show that `y=e^x(A\ cos x+Bsinx)` is the solution of the differential equation `(d^2y)/(dx^2)-2(dy)/(dx)+2y=0.`

Explanation

To show that \( y = e^x (A \cos x + B \sin x) \) is the solution of the differential equation

\[ \frac{d^2y}{dx^2} - 2\frac{dy}{dx} + 2y = 0, \]

we will follow these steps:

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