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Differential Equations question

2024 · 30 Jan · Shift 2 · Q52

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JEE Main
Mathematics
Differential Equations
2024 · 30 Jan · Shift 2 · Q52

Differential Equations question

2024 · 30 Jan · Shift 2 · Q52

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let

Y=Y(X)

be a curve lying in the first quadrant such that the area enclosed by the line

Y-y=Y^{\prime}(x)(X-x)

and the co-ordinate axes, where

(x, y)

is any point on the curve, is always

\frac{-y^2}{2 Y^{\prime}(x)}+1, Y^{\prime}(x) eq 0

. If

Y(1)=1

, then

12 Y(2)

equals

\underline{\hspace{2cm}}

.

Numerical answer

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