MATHEMATICA TUTORIAL

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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