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Determine order and degree (if defined) of differential equation (y′′′)2 + (y″)3 + (y′)4 + y5 = 0

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To determine the order and degree of the differential equation (y′′′)2+(y′′′)3+(y′′)4+y5=0(y′′′)2+(y′′′)3+(y′′)4+y5=0, let's first understand the terminologies: The order of a differential equation is...
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To determine the order and degree of the differential equation (y′′′)2+(y′′′)3+(y′′)4+y5=0(y′′′)2+(y′′′)3+(y′′)4+y5=0, let's first understand the terminologies:

  • The order of a differential equation is the highest order of the derivative present in the equation.
  • The degree of a differential equation is the highest power to which the highest-order derivative is raised.

In the given equation:

  • The highest-order derivative is y′′′y′′′, which is a third-order derivative. So, the order of the differential equation is 3.
  • The highest power of y′′′y′′′ is 3, so the degree of the equation with respect to y′′′y′′′ is 3.
  • There's no term directly involving y′′y′′, so we consider it as raised to the power of 1. Therefore, the degree of the equation with respect to y′′y′′ is 1.
  • There's no term directly involving y′y′, so we consider it as raised to the power of 0. Therefore, the degree of the equation with respect to y′y′ is 0.
  • The highest power of yy is 5, so the degree of the equation with respect to yy is 5.

Therefore, the differential equation (y′′′)2+(y′′′)3+(y′′)4+y5=0(y′′′)2+(y′′′)3+(y′′)4+y5=0 is a third-order differential equation and has a degree of 5.

 
 
 
 
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