Let y=f(x) be the solution of the differential equation dydx+ xyx2-1= x6+4x 1-x2, -1<x<1 such that f(0)=0. If 6 -1/21/2f(x) dx=2 - then 2 is equal to .
27
I.F. =e xx2-1dx= 1-x2
y 1-x2= x77+2x2+c
f(0)=0 c=0
On [- 12, 12 ] the odd part x77 1-x2 gives 0
6 -1/21/2 f dx=24 01/2 x2 1-x2dx
Put x= : =12 0 /6(1- 2 ) d
=12 ( 6- 34 )=2 -3 3
=3 3 2=27
Answer: 27
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