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

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4. Higher-Order Linear Ordinary Differential Equations

1. y′′′ + λy = 0.
2. y′′′ = ax^βy.
3. (x − a)³(x − b)³y′′′ − cy = 0.
4. (ax² + bx + c)³y′′′ = ky.
5. y′′′′ + ay = 0.
6. y′′′′ + axⁿy′′ + b(axⁿ − b)y = 0.
7. x²y′′′′ + 6xy′′′ + 6y′′ − a²y = 0.    Equation of transverse vibrations of a pointed bar.
8. (ax² + bx + c)⁴y′′′′ = ky.
9. y⁽⁶⁾ + ay = 0.
10. y⁽²ⁿ⁾ = a²ⁿy.
11. y⁽ⁿ⁾ = axy + b.
12. y⁽ⁿ⁾ = ax^βy.
13. (ax + b)ⁿ(cx + d)ⁿy⁽ⁿ⁾ = ky.
14. (ax² + bx + c)ⁿy⁽ⁿ⁾ = ky.
15. a_ny⁽ⁿ⁾ + a_{n − 1}y^{(n − 1)} + ... + a₁y′ + a₀y = 0.    Constant coefficient linear equation.
16. a_nxⁿy⁽ⁿ⁾ + a_{n − 1}x^{n − 1}y^{(n − 1)} + ... + a₁xy′ + a₀y = 0.    Euler equation.