CUET · MATHS · PYQ PAPER 2023
The differential equation whose solution is \(A x^2+B y^2=1\) where \(A\) and \(B\) are arbitrary constant is of:
(A) first order and first degree
(B) second order and first degree
(C) second order and second degree
(D) second order
Choose the correct answer from the options given below :
- A (D) Only
- B (C) and (D) Only
- C (B) and (D) Only
- D (A) Only
Answer & Solution
Correct Answer
(C) (B) and (D) Only
Step-by-step Solution
Detailed explanation
\(A x^2+B y^2=1\) \(2Ax + 2By y' = 0 \implies Ax + By y' = 0\) \(A + B(y'^2 + y y'') = 0\) From \(Ax + By y' = 0 \implies A/B = -yy'/x\) From \(A + B(y'^2 + y y'') = 0 \implies A/B = -(y'^2 + y y'')\) \(-yy'/x = -(y'^2 + y y'')\) \(yy' = x(y'^2 + y y'')\)…
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