Consider the following statements: 1. The degree of the differential equation \frac{dy}{dx}+\cos(\frac{dy}{dx})=0 is 1. 2. The order of the differential equation (\frac{d^{2}y}{dx^{2}})^{3}+\cos(\frac{dy}{dx})=0 is 2. Which of the statements given above is/are correct?
- A. 1 <strong>ONLY</strong>
- B. 2 <strong>ONLY</strong> ✓
- C. <strong>BOTH</strong> 1 and 2
- D. <strong>NEITHER</strong> 1 nor 2
Correct Answer: B. 2 <strong>ONLY</strong>
Explanation
In statement 1, the differential equation cannot be expressed as a polynomial of derivatives due to the \cos(\frac{dy}{dx}) term, so its degree is not defined (Statement 1 is false). In statement 2, the highest order derivative present is \frac{d^2y}{dx^2}, making the order 2 (Statement 2 is true).
Related questions on Calculus
- Let z=[y] and y=[x]-x, where [.] is the greatest integer function. If x is <strong>NOT</strong> an integer but positive, then what i...
- If f(x)=4x+1 and g(x)=kx+2 such that fog(x)=gof(x), then what is the value of k?
- What is the <strong>MINIMUM</strong> value of the function f(x)=\log_{10}(x^{2}+2x+11)?
- What is \int(x^{x})^{2}(1+\ln x)\,dx equal to ?
- What is \int e^{x}\{1+\ln x+x\ln x\}\,dx equal to?