Determine order and degree (if defined) of differential equation\(\Big(\frac{d^2y}{dx^2}\Big)\\^2+\cos\Big(\frac{dy}{dx}\Big)=0\)
Determine order and degree (if defined) of differential equation\(\Big(\frac{d^2y}{dx^2}\Big)\\^2+\cos\Big(\frac{dy}{dx}\Big)=0\)
Solution and Explanation
\(\Big(\frac{d^2y}{dx^2}\Big)\\^2+\cos\Big(\frac{dy}{dx}\Big)=0\)
The highest order derivative present in the given differential equation is \(\frac{d^2y}{dx^2}\) .
Therefore, its order is 2.
The given differential equation is not a polynomial equation in its derivatives.
Hence, its degree is not defined.
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Concepts Used:
Order and Degree of Differential Equation
The equation that helps us to identify the type and complexity of the differential equation is the order and degree of a differential equation.
The Order of a Differential Equation:
The highest order of the derivative that appears in the differential equation is the order of a differential equation.
The Degree of a Differential Equation:
The highest power of the highest order derivative that appears in a differential equation is the degree of a differential equation. Its degree is always a positive integer.
For examples:
- 7(d4y/dx4)3 + 5(d2y/dx2)4+ 9(dy/dx)8 + 11 = 0 (Degree - 3)
- (dy/dx)2 + (dy/dx) - Cos3x = 0 (Degree - 2)
- (d2y/dx2) + x(dy/dx)3 = 0 (Degree - 1)