Determine order and degree (if defined) of differential equation \(\frac{d^2y}{dx^2}=\cos 3x+\sin3x\)
Determine order and degree (if defined) of differential equation \(\frac{d^2y}{dx^2}=\cos 3x+\sin3x\)
Solution and Explanation
\(\frac{d^2y}{dx^2}=\cos 3x+\sin3x\)
\(\Rightarrow\frac{d^2y}{dx^2}-\cos3x-\sin3x=0\)
The highest order derivative present in the differential equation is \(\frac{d^2y}{dx^2}.\)
Therefore, its order is two.
It is a polynomial equation in \(\frac{d^2y}{dx^2}\) and the power raised to \(\frac{d^2y}{dx^2}\) is 1.
Hence, its degree is one.
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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)