CUET · MATHS · PYQ PAPER 2023
The general solution of the differential equation \(y d x-\left(x+2 y^2\right) d y=0\) is:
- A \(x=2 y^2+C_y, C\) is a constant
- B \(y=2 x^2+C_y, C\) is a constant
- C \(y=2 x^2+C_x, C\) is a constant
- D \(x=2 x^2+C_y, C\) is a constant
Answer & Solution
Correct Answer
(A) \(x=2 y^2+C_y, C\) is a constant
Step-by-step Solution
Detailed explanation
\(\frac{dx}{dy} - \frac{1}{y} x = 2y\) \(IF = e^{\int -\frac{1}{y} dy} = \frac{1}{y}\) \(\frac{d}{dy}\left(\frac{x}{y}\right) = 2\) \(\frac{x}{y} = 2y + C\) \(x = 2y^2 + Cy\)
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