The degree and order of the differential equation :
`2(d^(2)y)/(dx^(2))-3(dy)/(dx)+y=0` is :

Options

A. (2, 1)
B. (1, 2)
C. (2, 2)
D. Not defined

Answer

To determine the degree and order of the given differential equation:

**Given Differential Equation:**
\[ 2\frac{d^2y}{dx^2} - 3\frac{dy}{dx} + y = 0 \]

**Step 1: Identify the Order of the Differential Equation**
- The order of a differential equation is defined as the highest derivative present in the equation.
- In the given equation, we have:
- The term \(\frac{d^2y}{dx^2}\) which is the second derivative.
- The term \(\frac{dy}{dx}\) which is the first derivative.
- The highest derivative here is \(\frac{d^2y}{dx^2}\), which is the second derivative.

**Conclusion for Step 1:**
- Therefore, the order of the differential equation is **2**.

**Step 2: Identify the Degree of the Differential Equation**
- The degree of a differential equation is defined as the power of the highest derivative when the equation is a polynomial in derivatives.
- In the given equation, the highest derivative is \(\frac{d^2y}{dx^2}\) and it appears with a coefficient of 2.
- The power of this highest derivative is 1 (since \(2\frac{d^2y}{dx^2}\) can be expressed as \(2 \cdot (\frac{d^2y}{dx^2})^1\)).

**Conclusion for Step 2:**
- Therefore, the degree of the differential equation is **1**.

**Final Answer:**
- The order of the differential equation is **2** and the degree is **1**.

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