Home | 18.01 | Chapter 15 | Section 15.1

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Antiderivatives are not unique; any function has a family of  them which differ by constants among them.

Similarly differential equations have families of solutions, which however can differ in more complicated ways from one another. Extra conditions (like the lower limit in the definite integral) are necessary to specify an explicit solution. Usually one value anywhere is enough to specify a solution to a first order differential equation (the type considered here.)