InterviewSolution
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InterviewSolution
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If `y={x+sqrt(x^2+1)}^m`, show that `(x^2+1)y_2+x y_1-m^2 y=0`A. `m^(2)y`B. `my^(2)`C. `m^(2)y^(2)`D. none of these |
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Answer» Correct Answer - A We have, `y^(1//m)={x+sqrt(1+x^(2))}` `impliesy={x+sqrt(1+x^(2))}^(m)` `implies(dy)/(dx)=m{x+sqrt(1+x^(2))}^(m-1){1+(x)/(sqrt(x^(2)+1))}=m({xsqrt(1+x^(2))}^(m))/(sqrt(1+x^(2)))` `implies" "(dy)/(dx)=(my)/(sqrt(1+x^(2)))` `impliesy_(1)""^(2)(1+x^(2))=m^(2)y^(2)` `implies2y_(1)y_(2)(1+x^(2))+2xy_(1)""^(2)=2m^(2)yy_(1)` `impliesy_(2)(1+x^(2))+y_(1)=m^(2)y` |
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