InterviewSolution
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InterviewSolution
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If a curve `y=f(x)`passes through the point `(1,-1)`and satisfies the differentialequation `,y(1+x y)dx""=x""dy`, then `f(-1/2)`is equal to:(1) `-2/5`(2) `-4/5`(3) `2/5`(4) `4/5`A. `-(2)/(5)`B. `-(4)/(5)`C. `(2)/(5)`D. `(4)/(5)` |
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Answer» Correct Answer - D The differential equation is `y(1+xy)dx=xdy` `rArr" "ydx-xdy=-xy^(2)dx` `rArr" "(ydx-xdy)/(y^(2))=-xdx` `rArr" "d((x)/(y))=-xdx` On integrating, we obtain `(x)/(y)=-(x^(2))/(2)+C` It is given that the curve given by (i) passes though the point `(1,-1)` `therefore" "-1=-(1)/(2)+CrArr C=-(1)/(2)` Putting `C=-(1)/(2)` in (i), we obtain `y(x^(2)+1)+2x=0` Putting `x=-(1)/(2)` in (ii), we obtain `y=(4)/(5)`. Hence, `f(-(1)/(2))=(4)/(5)` |
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