## Ordinary Differential Equations: An IntroductionA textbook that is suitable for Undergraduate, Honours and Engineering courses that presupposes no background other than elementary calculus. |

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### Contents

Solvable First Order Equations | 13 |

Applications of First Order Equations | 53 |

Theoretical Considerations | 73 |

Linear Differential Equations I | 103 |

Linear Differential Equations II | 154 |

Systems of Differential Equations | 214 |

Numerical Methods | 229 |

Answers to Selected Exercises | 256 |

269 | |

### Common terms and phrases

approximate value arbitrary constants auxiliary equation Bernoulli's equation chapter circuit Clairaut's equation consider constant coefficients continuous corresponding homogeneous equation degree equation with constant error Example Exercise existence and uniqueness family of curves family of solution formula Forp fundamental system given differential equation given equation gives Hence homogeneous linear equation Improved Euler method independent variable initial value problem integrating factor interval isoclines linear differential equation linear equation linearly independent linearly independent solutions mass method of variation molecules nonhomogeneous observe obtained one-parameter family order linear equation orthogonal trajectory oscillation p-discriminant particular solution polynomial Proof roots Runge-Kutta method satisfy singular solution slope solution curve solution of 6.52 solutions of 5.18 substance Taylor series Theorem unique solution uniqueness of solutions variation of parameters velocity Wronskian y)dx y)dy yp(x zero