CUET · MATHS · PYQ PAPER 2025
Let \(e^{\alpha y}+e^{\beta y}+\gamma x^2+\delta \log |x|+C=0\), where \(C \in R ,\) be a particular solution of the differential equation
\(x\left(e^{2 y}-1\right) d y+\left(x^2-1\right) e^y d x=0\) and passes through the point \((1,1)\).
The value of \((\alpha+\beta+\gamma+\delta-C)\) is:
- A \(e-1\)
- B \(e^2-1\)
- C \(e+\frac{1}{e}\)
- D \(\frac{1}{e}\)
Answer & Solution
Correct Answer
(C) \(e+\frac{1}{e}\)
Step-by-step Solution
Detailed explanation
\(x\left(e^{2 y}-1\right) d y+\left(x^2-1\right) e^y d x=0\) \(\frac{e^{2y}-1}{e^y} d y+\frac{x^2-1}{x} d x=0\) \(\left(e^y-e^{-y}\right) d y+\left(x-\frac{1}{x}\right) d x=0\) \(\int\left(e^y-e^{-y}\right) d y+\int\left(x-\frac{1}{x}\right) d x=K\)…
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