JEE Mains · Maths · STD 12 - 9. differential equations
Let \(\alpha|\mathrm{x}|=|\mathrm{y}| \mathrm{e}^{\mathrm{xy}-\beta}, \alpha, \beta \in \mathrm{N}\) be the solution of the differential equation \(x d y-y d x+x y(x d y+y d x)=0\), \(y(1)=2\). Then \(\alpha+\beta\) is equal to ...........
- A \(4\)
- B \(5\)
- C \(9\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\( a|x|=|y| e^{y x-\beta}, a, b \in N \) \( x d y-y d x+x y(x d y+y d x)=0 \) \( \frac{d y}{y}-\frac{d x}{x}+(x d y+y d x)=0 \) \( \ell n|y|-\ell n|x|+x y=c \) \( y(1)=2 \) \( \ell n|2|-0+2=c \) \( c=2+\ell n 2 \) \( \ell n|y|-\ell n|x|+x y=2+\ell n 2 \)…
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