# Equations with Non-Rational Coefficients

The ODEs that arise in practical applications often have non-rational coefficients. In such cases, DSolve attempts to convert the equation into one with rational coefficients using a suitable coordinate transformation.

Here is an equation that has

Exp[x] as a coefficient. It is solved by transforming it to Bessel's equation.

Out[1]= | |

This equation (equation 2.437, page 507 of [

K59]) has trigonometric coefficients. The solution is given in terms of elementary functions.

Out[2]= | |

Here is an equation with a hyperbolic function in the coefficient of

. The solution is given in terms of Legendre functions.

Out[3]= | |

Out[5]= | |

This verifies the solution using random values of

,

,

, and

.

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