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Question

Form the differential equation for y=(sin1x)2+Acos1x+B where A and B are arbitary constants, as its general solution.
 


Solution

Given that, y=(sin1x)2+Acos1x+B
On differentiating w.r.t. x, we get
dydx=2sin1x1x2+(A)1x21x2dydx=2sin1xA
Again, differentiating w.r.t.x we get
1x2d2ydx2+dydx.2x21+x2=21x2(1x2)d2ydx2x1x2.1x2dydx=2(1x2)d2ydx2xdydx=2(1x2)d2ydx2xdydx2=0
which is the required differential equation. 

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