Let y=y(x) be the solution of the differential equation \frac{d y}{d x}+\frac{2 x}{ (1+x^2) ^2} y=x e^{\frac{1}{ (1+x^2) }} ; y(0)=0. Then the area enclosed by the curve f(x)=y(x) e^{\frac{1}{ (1+x^2) }} and the line y-x=4 is ______. [5 Apr 2024 Shift 2]

Differential Equations Part 2

Section: Mathematics

Question : 9 of 100

Marks: +1, -0

Let y=y(x) be the solution of the differential equation ‌

+‌

(1+x2)2

y=xe‌

(1+x2)

;y(0)=0. Then the area enclosed by the curve f(x)=y(x)e‌

(1+x2)

and the line y−x=4 is ______.

[5 Apr 2024 Shift 2]

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