CUET · MATHS · PYQ PAPER 2025
Which of the following statements is/are true?
(A) \(\left(\tan ^{-1} y-x\right) d y=\left(1+y^2\right)\) dx is a differential equation where variables are separable.
(B) (1+ \(x^2\))dy + 2xydx = cot xdx(x ≠ 0) is a first order linear differential equation.
(C) (4x + 6y + 5)dy - (3y + 2x + 4)dx = 0 is not a homogeneous differential equation.
(D) (xy)dx - (x + \(\left.y^2\right)\)dy = 0 is a homogeneous differential equation.
Choose the correct answert from the option given below :
- A (A) only
- B (B) and (C) only
- C (B) and (D) only
- D (A), (B), (C) and (D)
Answer & Solution
Correct Answer
(B) (B) and (C) only
Step-by-step Solution
Detailed explanation
(A) \(\left(\tan ^{-1} y-x\right) d y=\left(1+y^2\right) dx \implies \frac{dy}{dx} = \frac{1+y^2}{\tan^{-1}y - x}\). Not separable. (A) is false. (B) \((1+x^2)dy + 2xydx = \cot xdx\). \((1+x^2)\frac{dy}{dx} + 2xy = \cot x\).…
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