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The solution of the differential equation `(1+y^(2)) tan^(-1) x dx + y(1+x^(2)) dy = 0` isA. `log((tan^(-1)x)/(x)) + y(1+x^(2)) =0`B. `log ((tan^(-1)x)/(x)) + y(1+x^(2))= c`C. `log (1+x^(2)) + log (tan^(-1)y) + c`D. `(tan^(-1) x) (1+y^(2))+c=0` |
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Answer» Correct Answer - B Given `(tan^(-1)x)/(1+x^(2)) dx + (y)/(1+y^(2)) dy = 0` integrating both sides , we get `rArr ((tan^(-1)x)^(2))/(2) +(1)/(2)log(1+y^(2)) = (C)/(2)` ` rArr (tan^(-1) x)^(2) + log (1+y^(2)) = c` |
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