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More About Solutions



Differential equations have two kinds of solutions: general and particular.

The general solution to a differential equation is the collection of all solutions to that differential equation. A general solution will usually contain some undetermined constants.

Sample Problem

y = 4x + C is the general solution to the d.e.

' = 4.

Sample Problem

y = 3x2 + Bx + C is the general solution to the d.e.

" = 6.

A particular solution to a differential equation is a solution with all the constants filled in.

Sample Problem

The function y = 4x + 2 is a specific solution to the d.e.

' = 4.

Initial value problems usually have a particular solution only, because the initial condition(s) force us to pick values for the constant(s) in the general solution.

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