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