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In This Chapter
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Chapter 15: Third-Order Ordinary Differential Equations
- Linear Equations
- Preliminary Remarks
- Equations Containing Power Functions
- Equations Containing Exponential Functions
- Equations Containing Hyperbolic Functions
- Equations Containing Logarithmic Functions
- Equations Containing Trigonometric Functions
- Equations Containing Inverse Trigonometric Functions
- Equations Containing Combinations of Exponential, Logarithmic, Trigonometric, and Other Functions
- Equations Containing Arbitrary Functions
- Equations of the Form y x x x ″ ′ = A x α y β ( y x ′ ) γ ( y x x ″ ) δ $ y^{\prime\prime\prime}_{xxx} = Ax^{\alpha } y^{\beta } (y^{\prime}_{x} )^{\gamma } (y^{\prime\prime}_{xx} )^{\delta } $
- Classification Table
- Equations of the Form y x x x ″ ′ = A y β $ y_{xxx}^{\prime\prime\prime} = Ay^{\beta } $
- Equations of the Form y x x x ″ ′ = A x α y β $ y_{xxx}^{\prime\prime\prime} = Ax^{\alpha } y^{\beta } $
- Equations with |γ| + |δ| ≠ 0
- Some Transformations
- Equations of the Form y x x x ″ ′ = f ( y ) g ( y x ′ ) h ( y x x ″ ) $ y_{xxx}^{\prime\prime\prime} = f(y)g(y_{x}^{\prime} )h(y_{xx}^{\prime\prime} ) $
- Nonlinear Equations with Arbitrary Parameters
- Equations Containing Power Functions
- Equations Containing Exponential Functions
- Equations Containing Hyperbolic Functions
- Equations Containing Logarithmic Functions
- Equations Containing Trigonometric Functions
- Nonlinear Equations Containing Arbitrary Functions
- Equations of the Form F ( x , y ) y x x x ″ ′ + G ( x , y ) = 0 $ F(x, y)y^{\prime\prime\prime}_{xxx} + G(x, y) = 0 $
- Equations of the Form F ( x , y , y x ′ ) y x x x ″ ′ + G ( x , y , y x ′ ) = 0 $ F(x, y, y_{x}^{\prime} )y_{xxx}^{\prime\prime\prime} + G(x, y, y_{x}^{\prime} ) = 0 $
- Equations of the Form
- Equations of the Form
- Other Equations
Abstract
1 o . A homogeneous linear equation of the third order has the general form 1 f 3 ( x ) y x x x ″ ′ + f 2 ( x ) y x x ″ + f 1 ( x ) y x ′ + f 0 ( x ) y = 0 . $$ f_{3} (x)y_{{xxx}}^{{\prime\prime\prime}} + f_{2} (x)y_{{xx}}^{{\prime\prime}} + f_{1} (x)y_{x}^{\prime} + f_{0} (x)y = 0 . $$
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