Let y=y(x) be the solution of the differential equation (1-x^2) d y=(x y+(x^3+2) \sqrt{1-x^2}) d x,-1< x< 1, and y(0)=0 . If \int_{\frac{-1}{2}}^{\frac{1}{2}} \sqrt{1-x^2} y(x) d x=k, then {\k}^{-1} is equal to____ [27-Jun-2022-Shift-2]

Differential Equations Part 2

Section: Mathematics

Question : 85 of 100

Marks: +1, -0

Let y=y(x) be the solution of the differential equation (1−x2)dy=(xy+(x3+2)√1−x2)dx,−1<x<1, and y(0)=0. If

‌

∫

‌

−1

√1−x2y(x)dx=k, then k−1 is equal to____

[27-Jun-2022-Shift-2]

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