CUET · MATHS · PYQ PAPER 2023
Solution of the differential equation \(\frac{d y}{d x}+\frac{3 x}{2 y}=0\) with y(1) = 1 is:
- A \(2 y^2+3 x^2=5\)
- B \(3 x^2-2 y^2=5\)
- C \(2 x^2+3 y^2-5=0\)
- D \(2 x^2+3 y^2+5=0\)
Answer & Solution
Correct Answer
(A) \(2 y^2+3 x^2=5\)
Step-by-step Solution
Detailed explanation
\(2y \, dy = -3x \, dx\) \(\int 2y \, dy = \int -3x \, dx\) \(y^2 = -\frac{3}{2}x^2 + C\) \(2y^2 + 3x^2 = C_1\) \(2(1)^2 + 3(1)^2 = C_1 \Rightarrow 2+3=C_1 \Rightarrow C_1=5\) \(2y^2+3x^2=5\)
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