7

Initial Value Problems

Solve y′ =F(x,y) with the auxiliary conditions y(a)=α |

The general form of a first-order differential equation is

(7.1a) |

where y′ =dy/dx and f(x,y) is a given function. The solution of this equation contains an arbitrary constant (the constant of integration). To find this constant, we must know a point on the solution curve; that is, y must be specified at some value of x, say at x = a. We write this auxiliary condition as

(7.1b) |

An ordinary differential equation of order n

(7.2) ... |

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