## Intermediate differential equations |

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### Contents

Linear Equations of Order Two 1 Elementary methods | 1 |

Change of dependent variable | 2 |

The normal form | 7 |

Copyright | |

94 other sections not shown

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### Common terms and phrases

analytic at z0 arbitrary constants Bessel functions Bessel's equation canonical form Cauchy product coefficients complete solution convergence corresponding denominator derivative determined elementary equation of Ex equation of order essential singular point EXAMPLE Exercises exponents factor finite plane follows formula Fuchsian equation Hence Hermite polynomials hypergeometric equation hypergeometric function independent variable indicial equation Jn(z Laguerre polynomials Legendre polynomials Legendre's equation linear equation linearly independent linearly independent solutions logarithmic solution maps multiply negative integer notation numerator obtain ordinary point P-symbol parameter particular solution point of equation pole of order polynomial solutions positive integer problem prove recurrence relation region of validity regular singular point result Riccati equation right member roots Show solution of equation solutions valid Solve the equation table of Rummer's Theorem 27 three singular points transformation Whittaker's equation write yields z-plane zero