If y = ex.tan-1x,prove that (1+x2)y2 2(1-x+x2)y1 + (1-x2)y = 0

  • -1
  • y = ex. tan-1x
  • y1 = ex (tan-1x + 1/(1+x2) )
  • y1.(1+x2) = ex + ex.tan-1x.(1+x2)
  • y1.(1+x2) = ex + y.(1+x2)
  • y2.(1+x2) + y1(2x) = ex + y1(1+x2) + y(2x)
  • y2.(1+x2) + y1(2x)=(y1.(1+x2) - y.(1+x2)) + y1(1+x2) + y(2x)
  • (1+x2)y2 - 2(1-x+x2)y1 + (1-x)2y= 0

This expression seems quite different from the one used asked to 'prove', but should be correct.

  • 24
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