Exact Solutions > Ordinary Differential Equations > Higher-Order Linear Ordinary Differential Equations

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5. Higher-Order Nonlinear Ordinary Differential Equations

1. y′′′ = Ax^αy^β.    Emden--Fowler equation of the third-order.
2. y′′′ = ay^{− 5/2} + by^{− 7/2}.
3. y′′′ = f(y).
4. yy′′′ = f(x).
5. y′′′′ = Ay^{− 5/3}.
6. y′′′′ = f(y).
7. F(x, y′, y′′, ..., y⁽ⁿ⁾) = 0.    The equation does not depend on y explicitly.
8. F(y, y′, y′′, ..., y⁽ⁿ⁾) = 0.    Autonomous equation.
9. F(x, xy′′ − my, y^(m+1), y^(m+2), ..., y⁽ⁿ⁾) = 0,    m = 1, 2, ..., n − 1.
10. F(x^ky^m, xy′/y, x²y′′/y, ..., xⁿy⁽ⁿ⁾/y) = 0.    Generalized homogeneous equation.
11. F(e^αxy^m, y′/y, y′′/y, ..., y⁽ⁿ⁾/y) = 0.
12. F(x^me^αy, xy′, x²y′′, ..., xⁿy⁽ⁿ⁾) = 0.