Ordinary Differential Equations by Tenenbaum & Pollard

ODE by Tenenbaum & Pollard, Exercise 3, Problem 1

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Problem

Determine the order of the following differential equations.

  1. dy + ( xy - \cos{x} ) dx = 0
  2. y^{\prime\prime} + x y^{\prime\prime} + 2y ( y^{\prime} )^3 + xy = 0
  3. (\frac{d^2y}{dx^2})^3 - (y^{\prime\prime\prime})^4 + x = 0
  4. e^{y^{\prime\prime\prime}} + x y^{\prime\prime} + y = 0

Solution

dy + ( xy - \cos{x} ) dx = 0

This is order 1.

 

y^{\prime\prime} + x y^{\prime\prime} + 2y ( y^{\prime} )^3 + xy = 0

This is order 2.

 

(\frac{d^2y}{dx^2})^3 - (y^{\prime\prime\prime})^4 + x = 0

This is order 3.

 

e^{y^{\prime\prime\prime}} + x y^{\prime\prime} + y = 0

This is order 3.

 

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