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Differential Equations question

2024 · 5 Apr · Shift 2 · Q51

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JEE Main
Mathematics
Differential Equations
2024 · 5 Apr · Shift 2 · Q51

Differential Equations question

2024 · 5 Apr · Shift 2 · Q51

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let

y=y(x)

be the solution of the differential equation

\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{2 x}{\left(1+x^2\right)^2} y=x \mathrm{e}^{\frac{1}{\left(1+x^2\right)}} ; y(0)=0.

Then the area enclosed by the curve

f(x)=y(x) \mathrm{e}^{-\frac{1}{\left(1+x^2\right)}}

and the line

y-x=4

is

\underline{\hspace{2cm}}

.

Numerical answer

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