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Diff. W.r t. X Y=√1-x/1+x TO …

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Diff. W.r t. X Y=√1-x/1+x TO prove that (1-x^2)dy/dx+y=0

Posted by Shruti Rajput 7 years, 5 months ago

CBSE > Class 12 > Mathematics

1 answers

Harish Nagar 7 years, 5 months ago

dy/dx =1/2(1-x/1+x)^1/2-1×d/dx(1-x/1+x) => dy/dx= 1/2underroot (1+x/1-x)×(1+x)d/dx(1-x)-(1-x)d/dx(1+x)/(1+x)^2 => dy/dx=1/2undroot(1+x/1-x)×(1+x)(-1)-(1-x)(1)/(1+x)^2 => dy/dx =1/2undroot(1+x/1-x)×-1-x-1+x/(1+x)^2 => dy/dx =-undroot (1+x/1-x)×1/(1+x)^2 => (1-x^2)dy/dx =-undroot (1+x)/(1-x)×1/(1+x)^2×(1-x^2) => (1-x^2)dy/dx =- undroot (1+x)/1-x) => (1+x^×)dy/dx =-y => (1-x^2)dy/dx +y=0 Hence proved Its very simple question ok

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