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MATHMAA

# Order Of Differential Equation

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