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Order Of Differential Equation

Probability Introduction :

ORDER OF DIFFERENTIAL EQUATION:

 Definition:

                       A differential equation is said to be of order n, if the nth derivative is the highest derivative in that equation.

Examples:

1.  \[\left ( 2x^{2}+1 \right )\frac{dy}{dx}+3xy =5x^{2}\]

The first derivative dy/dx is the highest derivative in the above equation.

Therefore the order of the above differential equation is 1.


2. \[x\frac{d^{2}y}{dx^{2}}-\left ( 3x+2 \right )+y=3e^{x}\]

The second derivative d^2y/dx^2 is the highest derivative in the above equation.

Therefore the order of the above differential equation is 2.


In general, differential equation of order 'n' is of the form \[F\left ( x,y,{y}',{y}''\cdots y^{(n)} \right )= 0\]

Differential Equations


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