## Ordinary differential equations |

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### Contents

INTRODUCTION | 1 |

FIRSTORDER DIFFERENTIAL | 15 |

LINEAR DIFFERENTIAL EQUATIONS | 31 |

Copyright | |

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### Common terms and phrases

arbitrary arctan boundary-value problem bounded change of variables Chapter characteristic polynomial chit z condition CieriX constant coefficients continuous function continuously differentiable curve through P0 derivative differentiable function differential equation y1 dy/dx end points ential equation equa equation L(y equicontinuous eriX Euler's formula Examples Exercise existence theorem f satisfies family of curves ferential equation find a solution Find the solution first-order differential equation first-order equation function y(x given point x0 global Lipschitz condition Hence homogeneous equation inhomogeneous initial values initial-value problem instance integral equation linear differential equation linear space Lips chit lution mean value theorem n^-Order open interval original equation Partial Differential Equations Peano existence theorem polygon proof prove real-valued function ri and r2 satisfies a global set of solutions solu solution curve Solve the differential tangent trigonometric function unique solution uniquely determined vector whole plane written ye(x zero