SECTION 1.4 Newton\'s First and Second Laws; Inertial Frames 1.24 In case you ha
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SECTION 1.4 Newton's First and Second Laws; Inertial Frames 1.24 In case you haven't studied any differential equations before, I shall be introducing the necessary ideas as needed. Here is a simple excercise to get you started: Find the general solution of the first- order equation df/dt = f for an unknown function f(t). [There are several ways to do this. One is to rewrite the equation as df/f = dt and then integrate both sides.] How many arbitrary constants does the general solution contain? [Your answer should illustrate the important general theorem that the solution to any nth-order differential equation (in a very large class of "reasonable" equations) contains n arbitrary constants.] 1.25 Answer the same questions as in Problem 1.24, but for the differential equation df /di--3fExplanation / Answer
df/dt = -3f
df/f = -3dt
integrating both sides we get
log(f) = -3t + C .... C is a constant that needs to be included everytime you make an integration. It's value can be found only if some known relative values of f and t are given
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