CUET · MATHS · PYQ PAPER 2025
The general solution of the differential equation \(y d x-\left(x+2 y^2\right) d y=0\) is:
- A \(\frac{x}{y}=2 x+C\), Where C is constant of integration
- B \(y=2 x^2+C\), Where C is constant of integration
- C \(\frac{y}{x}=2 y+C\), Where C is constant of integration
- D \(x=2 y^2+C y\), Where \(C\) is constant of integration
Answer & Solution
Correct Answer
(D) \(x=2 y^2+C y\), Where \(C\) is constant of integration
Step-by-step Solution
Detailed explanation
\(\frac{dx}{dy} - \frac{1}{y}x = 2y\) \(IF = e^{\int -\frac{1}{y} dy} = e^{-\ln y} = \frac{1}{y}\) \(x \cdot \frac{1}{y} = \int 2y \cdot \frac{1}{y} dy\) \(\frac{x}{y} = \int 2 dy\) \(\frac{x}{y} = 2y + C\) \(x = 2y^2 + Cy\)
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