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Ordinary Differential Equations >
HigherOrder Linear Ordinary Differential Equations
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5. HigherOrder Nonlinear Ordinary Differential Equations

y′′′ = Ax^{α}y^{β}.
EmdenFowler equation of the thirdorder.

y′′′ = ay^{− 5/2} + by^{− 7/2}.

y′′′ = f(y).

yy′′′ = f(x).

y′′′′ = Ay^{− 5/3}.

y′′′′ = f(y).

F(x, y′, y′′, ..., y^{(n)}) = 0.
The equation does not depend on y explicitly.

F(y, y′, y′′, ..., y^{(n)}) = 0.
Autonomous equation.

F(x, xy′′ − my, y^{(m+1)}, y^{(m+2)}, ..., y^{(n)}) = 0, m = 1, 2, ..., n − 1.

F(x^{k}y^{m}, xy′/y, x^{2}y′′/y, ..., x^{n}y^{(n)}/y) = 0.
Generalized homogeneous equation.

F(e^{αx}y^{m}, y′/y, y′′/y, ..., y^{(n)}/y) = 0.

F(x^{m}e^{αy}, xy′, x^{2}y′′, ..., x^{n}y^{(n)}) = 0.
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