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The order and degree of differential equ...

The order and degree of differential equation: `[1+((dy)/(dx))^(2)]=(d^(2)y)/(dx^(2)""` are

A

`2,(3)/(2)`

B

2,3

C

2,1

D

3,4

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To find the order and degree of the given differential equation: \[ 1 + \left(\frac{dy}{dx}\right)^2 = \frac{d^2y}{dx^2} \] we will follow these steps: ### Step 1: Identify the derivatives present in the equation The equation contains two types of derivatives: - The first derivative: \(\frac{dy}{dx}\) - The second derivative: \(\frac{d^2y}{dx^2}\) ### Step 2: Determine the order of the differential equation The order of a differential equation is defined as the highest order of derivative present in the equation. Here, the highest order derivative is \(\frac{d^2y}{dx^2}\), which is a second derivative. Thus, the order of the differential equation is: \[ \text{Order} = 2 \] ### Step 3: Determine the degree of the differential equation The degree of a differential equation is defined as the highest power of the highest order derivative when the equation is expressed as a polynomial in derivatives. In our equation, the highest order derivative is \(\frac{d^2y}{dx^2}\), and it appears with a power of 1 (since it is not raised to any power). Thus, the degree of the differential equation is: \[ \text{Degree} = 1 \] ### Conclusion The order and degree of the given differential equation are: - **Order**: 2 - **Degree**: 1 ### Final Answer Order: 2, Degree: 1 ---
To find the order and degree of the given differential equation: \[ 1 + \left(\frac{dy}{dx}\right)^2 = \frac{d^2y}{dx^2} \] we will follow these steps: ### Step 1: Identify the derivatives present in the equation The equation contains two types of derivatives: ...
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