## DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONSPrimarily intended for the undergraduate students in Mathematics, Physics and Engineering, this text gives in-depth coverage of differential equations and the methods of solving them. The book begins with the basic definitions, the physical and geometric origins of differential equations, and the methods for solving first-order differential equations. Then it goes on to give the applications of these equations to such areas as biology, medical sciences, electrical engineering and economics. The text also discusses, systematically and logically, higher-order differential equations and their applications to telecom-munications, civil engineering, cardiology and detec-tion of diabetes, as also the methods of solving simultaneous differential equations and their applica-tions. Besides, the book provides a detailed discussion on Laplace transform and their applications, partial differential equations and their applications to vibration of a stretched string, heat flow, transmission lines, etc., and calculus of variations and its applications. This book, which is a happy fusion of theory and application, would also be useful to postgraduate students. |

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### Contents

DIFFERENTIAL EQUATIONS OF FIRST ORDER | 27 |

Exercises | 63 |

APPLICATIONS OF FIRST ORDER DIFFERENTIAL | 78 |

Exercises 755 | 155 |

HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS 162229 | 162 |

APPLICATIONS OF HIGHERORDER DIFFERENTIAL | 230 |

SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS | 299 |

LAPLACE TRANSFORMS AND THEIR APPLICATIONS | 353 |

Exercis es | 388 |

Exercises | 439 |

485 | |

507 | |

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amount amplitude applications arbitrary constants assume auxiliary equation beam boundary conditions cable calculus of variation capacitor compartment complete solution concentration constant of proportionality curve damping denote determine Differentiating Eq drug dt dt dx dx dx dy dx Solution dxldt dyldx equate the coefficients equilibrium position Euler's equation Example Fourier series ft/s function given differential equation given equation glucose Hence indicial equation initial conditions integrating factor Laplace transform linear differential equation linear equation mass maximum method Newton's second law obtain ordinary differential equation orthogonal trajectories partial differential equation problem radius reduces required solution respect roots Separating the variables simple harmonic motion Solution Let solution of Eq Solution The A.E. Solution The given Solve D2 spring Substituting tank temperature Theorem variables and integrating velocity vibrations voltage weight yields zero