JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Let

\alpha x=\exp \left(x^{\beta} y^{\gamma}\right)

be the solution of differential equation

2 x^{2} y d y-\left(1-x y^{2}\right) d x=0, x>0

y(2)=\sqrt{\log _{e} 2}

. Then

\alpha+\beta-\gamma

equals

View answer and explanation

Correct option: B

Option B is correct. Solving the differential equation and using the given condition, we find

\alpha=2, \beta=1, \gamma=2

, thus

\alpha+\beta-\gamma = 1

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