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.
This equation (equation 2.437, page 507 of [K59
]) has trigonometric coefficients. The solution is given in terms of elementary functions.
Here is an equation with a hyperbolic function in the coefficient of
. The solution is given in terms of Legendre functions.
This verifies the solution using random values of