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in this video were going to talk about how to solve first order linear differential equations now the first thing you need to do is you need to write it in standard form and that is y prime plus p of x times y which is equal to q of x now once you have it in standard form you need to identify the functions p of x and q of x now the next thing you need to do is determine the integrating factor which is e raised to the integral of p x dx now once you have the integrating factor you can now write the general solution to the differential equation so its going to be 1 divided by the integrated factor times the integral of i of x times q of x dx and then plus some constant of integration now once you integrate this portion to get the integrating factor and dont add the constant of integration you should only add it at the very end in this step so keep that in mind now lets work on some problems so lets say if we have this differential equation y prime plus 2y is equal to 2e to the x so
