Differential Equations/Second Order

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A differential equation of second order is of the form A(x)y'' + B(x)y' + C(x)y = g(x).

If g(x) = 0, then the equation is called homogeneous.

Contents 1 1: Constant Coefficients 2 2: Series Solutions 3 3: Hypergeometric Equations 4 4: Frobenius Solution to the Hypergeometric Equation 5 5: Legendre Equation 6 6: Bessel Equation 7 7: Mathieu Equation 8 8: Continued Fraction Solutions

[edit] 1: Constant Coefficients

A(x)=A; where A(x) is a function of x (or a variable), and A is a constant

[edit] 2: Series Solutions

[edit] 3: Hypergeometric Equations

[edit] 4: Frobenius Solution to the Hypergeometric Equation

[edit] 5: Legendre Equation

[edit] 6: Bessel Equation

[edit] 7: Mathieu Equation

[edit] 8: Continued Fraction Solutions