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In this video, the process for solving first order linear differential equations is explained. The first step is to write the equation in standard form, y' + p(x)y = q(x). Then, identify the functions p(x) and q(x). Next, find the integrating factor, e^(∫p(x)dx). With the integrating factor, the general solution is found as 1/integrating factor times the integral of integrating factor times q(x)dx. Finally, add the constant of integration at the end. The method is demonstrated using an example equation y' + 2y = 2e^x.