QJEEM19Ma5ebc: JEE Main 2019 Mathematics - Class 12 JEEM19Ma5ebc Solution: The curve amongst the family of curves represented by the…

Question

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The curve amongst the family of curves represented by the differential equation, (x² – y²)dx + 2xy dy = 0 which passes through (1, 1) is :

Accepted Answer

(x²

-

y²) dx + 2xy dy = 0

\frac{d y}{d x} = \frac{y^{2} - x^{2}}{2 x y}

Put

y = v x \Rightarrow \frac{d y}{d x} = v + x \frac{d v}{d x}

Solving we get,

\int \frac{2 v}{v^{2} + 1} d v = \int - \frac{d x}{x}

ln(v² + 1) =

-

ln x + C

(y² + x²) = Cx

1 + 1 = C

\Rightarrow

C = 2

y² + x² = 2x

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