If ydy/dx = x[ (y²)/(x²) + (φ ((y²)/(x²)))/(φ '((y²)/(x²))) ], x > 0, φ > 0, and y(1) = - 1, then φ ((y²)/4) is equal to:

Differential Equations: JEE Main 2021 Mathematics question

JEE Main 2021 · 31 Aug, Evening shift · Q3618

JEE Main 202131 Aug, Evening shiftMathematicsMediumDifferential Equations163× since 2002

y{{dy} \over {dx}} = x\left[ {{{{y^2}} \over {{x^2}}} + {{\phi \left( {{{{y^2}} \over {{x^2}}}} \right)} \over {\phi '\left( {{{{y^2}} \over {{x^2}}}} \right)}}} \right]

, x > 0,

\phi

> 0, and y(1) =

-

1, then

\phi \left( {{{{y^2}} \over 4}} \right)

is equal to :

JEE Main 2021 · 31 Aug, Evening shift · Q3618

JEE Main 202131 Aug, Evening shiftMathematicsMediumDifferential Equations163× since 2002

y{{dy} \over {dx}} = x\left[ {{{{y^2}} \over {{x^2}}} + {{\phi \left( {{{{y^2}} \over {{x^2}}}} \right)} \over {\phi '\left( {{{{y^2}} \over {{x^2}}}} \right)}}} \right]

, x > 0,

\phi

> 0, and y(1) =

-

1, then

\phi \left( {{{{y^2}} \over 4}} \right)

is equal to :