CUET · MATHS · PYQ PAPER 2025
For the differential equation \((x+y) d y+(x-y) d x=0\), which of the following is/are correct?
(A) Differential equation is homogeneous
(B) Order of differential equation is 1
(C) Integrating factor of differential equation is \(e ^{ x }\)
(D) Degree of the equation is not defined
Choose the correct answer from the options given below:
- A \((A)\) only
- B \((B)\), \((C)\) and \((D)\) only
- C \((A)\), \((B)\) and \((D)\) only
- D \((A)\) and \((B)\) only
Answer & Solution
Correct Answer
(D) \((A)\) and \((B)\) only
Step-by-step Solution
Detailed explanation
\((A)\) \(\frac{dy}{dx} = \frac{y-x}{x+y}\) \(f(tx,ty) = \frac{t(y-x)}{t(x+y)} = f(x,y)\). Statement (A) is correct. \((B)\) Highest derivative is \(\frac{dy}{dx}\). Order = 1. Statement (B) is correct. The correct answer is "\((A)\) and \((B)\) only".
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