If y = e^{x}.tan^{-1}x,prove that (1+x^{2})y_{2} 2(1-x+x^{2})y_{1} + (1-x^{2})y = 0 Share with your friends Share 10 Varun.Rawat answered this Refer the following link : https://www.meritnation.com/ask-answer/question/please-provide-a-solution-of-this-questio-as-ihave-stuck-to/continuity-and-differentiability/7240175 -1 View Full Answer Chinmaya answered this y = e^{x}. tan^{-1}xy_{1 }= e^{x} (tan^{-1}x + 1/(1+x^{2}) )y_{1}.(1+x^{2}) = e^{x }+ e^{x}.tan^{-1}x.(1+x^{2})y_{1}.(1+x^{2}) = e^{x }+ y.(1+x^{2})y_{2}.(1+x^{2}) + y_{1}(2x) = e^{x }+ y_{1}(1+x^{2}) + y(2x)y_{2}.(1+x^{2}) + y_{1}(2x)=(y_{1}.(1+x^{2}) - y.(1+x^{2})) + y_{1}(1+x^{2}) + y(2x)(1+x^{2})y_{2} - 2(1-x+x^{2})y_{1} + (1-x)^{2}y= 0 This expression seems quite different from the one used asked to 'prove', but should be correct. 24