InterviewSolution
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InterviewSolution
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If`y=sqrt((1-x)/(1+x)),p rov et h a t(1-x^2)(dy)/(dx)+y=0` |
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Answer» We have `y=sqrt((1-x)/(1+x))` Differentiating w.r.t.x, we get `(dy)/(dx)=(1)/(2)((1-x)/(1+x))^((1//2)-1)(d)/(dx)((1-x)/(1+x))` `=(1)/(2)sqrt((1+x)/(1-x))((1+x)(d)/(dx)(1-x)-(1-x)(d)/(dx)(1+x))/(1+x)^(2)=-sqrt((1+x)/(1-x))(1)/((1+x)^(2))` `"or " (1-x^(2))(dy)/(dx)=-sqrt((1+x)/(1-x))(1)/((1+x)^(2))(1-x^(2))` `"or " (1-x^(2))(dy)/(dx)=-sqrt((1-x)/(1+x))` `"or " (1-x^(2))(dy)/(dx)=-y` `"or " (1-x^(2))(dy)/(dx)+y=0` |
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