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Particular Solutions

Finding particular solutions using initial conditions and separation of variables.

Mapped to AP College Board # FUN-7, FUN-7.E, FUN-7.E.1, FUN-7.E.2, FUN-7.E.3

Solving differential equations allows us to determine functions and develop models. Determine particular solutions to differential equations. A general solution may describe infinitely many solutions to a differential equation. There is only one particular solution passing through a given point. The function F defined by F(x) = y0 + ∫f(t) dt for limit from a to x is a particular solution to the differential equation dy/dx = f(x), satisfying F(a) = y0. Solutions to differential equations may be subject to domain restrictions.