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The given differential equation is: \[ \frac{d^2y}{dx^2} - y = \frac{2}{1+e^x} \] We will solve it using the method of variation of parameters. ### Step 1: Find the Complementary Solution (Homogeneous Equation) The homogeneous equation associated with the given differential equation is: \[ \frac{d^2y}{dx^2} - y = 0 \] The characteristic equation is: \[ r^2 - 1 _________ _____ ________ _____ ______ _______ ________ _____ __________ ______.
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