CUET · MATHS · PYQ PAPER 2025
The solution of the differential equation \(\left(x^2+x y\right) d y=\left(x^2+y^2\right) d x\) is
- A \(y+\log _e\left|\frac{y-2}{x}\right|=c\),(c is an arbitrary constant)
- B \(\frac{y}{x}+\log _e\left|\frac{(y-x)^2}{x}\right|=c\), (c is an arbitrary constant)
- C \(y-\log _e\left|\frac{y-x}{x}\right|=c\),(c is an arbitrary constant)
- D \(y^2+\log _e\left|\frac{(y-x)^2}{x}\right|=c\),(c is an arbitrary constant)
Answer & Solution
Correct Answer
(B) \(\frac{y}{x}+\log _e\left|\frac{(y-x)^2}{x}\right|=c\), (c is an arbitrary constant)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = \frac{x^2+y^2}{x^2+xy} = \frac{1+(y/x)^2}{1+(y/x)}\) Let \(y=vx \Rightarrow \frac{dy}{dx}=v+x\frac{dv}{dx}\). Substituting: \(v+x\frac{dv}{dx} = \frac{1+v^2}{1+v} \Rightarrow x\frac{dv}{dx} = \frac{1-v}{1+v}\)…
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