The solution of the differential equation x2dydxcos1x−ysin1x=−1 When y→−1 as x→∞ is
y=sin(1x)−cos(1x)
y=x+1xsin(1x)
y=cos(1x)+sin(1x)
y=x+1xcos(1x)
dydx−yx2tan1x=−sec1x⋅1x2 I. F=e∫-1x2tan1xdx=eln sec1x=sec1x Solution of the D.E is ysec1x=−∫sec21x⋅1x2dxysec1x=tan1x+c........(1) Given y→−1 and x→∞-sec1∞=tan1∞+c -sec0=tan0+c c=−1substituting in (1)ysec1x=tan1x-1y=sin1x−cos1x