CUET · MATHS · PYQ PAPER 2025
The general solution of the differential equation \(\left(x^2-y x^2\right) d y+\left(y^2+x^2 y^2\right) d x=0\) is :
- A \(\log _e|y|+\frac{1}{x}+\frac{1}{y}-x=c\)
- B \(\log _e|y|-\frac{1}{x}+\frac{1}{y}+x=c\)
- C \(\log _e|x|-\frac{1}{x}+\frac{1}{y}+x=c\)
- D \(\log _e|x|+\frac{1}{x}+\frac{1}{y}+x=c\)
Answer & Solution
Correct Answer
(A) \(\log _e|y|+\frac{1}{x}+\frac{1}{y}-x=c\)
Step-by-step Solution
Detailed explanation
\(\left(x^2-y x^2\right) d y+\left(y^2+x^2 y^2\right) d x=0\) \(x^2(1-y) d y + y^2(1+x^2) d x = 0\) \(\frac{1-y}{y^2} d y = -\frac{1+x^2}{x^2} d x\) \(\left(\frac{1}{y^2}-\frac{1}{y}\right) d y = -\left(\frac{1}{x^2}+1\right) d x\)…
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