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To solve the given differential equation \( y' - y = 2e^x \) numerically, we can use a method like Euler's method or Runge-Kutta method. However, to find the particular integral, we can first solve the equation analytically. ### Step 1: Solve the homogeneous equation The homogeneous form of the equation is: \[ y' - y = 0 \] This can be solved by separating variables or recognizing it as a first-order linear differential equation: \[ y' = y \] The general solution to this is: \[ y_h = C e^x \] __________ _______ _______ ______ _________ _________ _______ _____ ____ ___ ___.
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