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To solve the given differential equation \( y'' - y = 2e^x \), we will use the method of solving non-homogeneous linear differential equations. ### Step 1: Solve the homogeneous equation The homogeneous equation is: \[ y'' - y = 0 \] The characteristic equation is: \[ r^2 - 1 = 0 \quad \Rightarrow \quad r = \pm _______ __________ _________ ________ _____ __________ _________ __________ _____.
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