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The solution of the differential equation `(x^(2)+4y^(2)-5)xd=(4x^(2)-3y^(2)-1)ydy`isA. `2/(sqrt(3))tan^(-1)(sqrt(3)((y^(2)-1)/(x^(2)-1)))-1/4 "In" (6((y^(2)-1)/(x^(2)-1))^(2)+2)-"In"sqrt(|x^(2)-1|)+c=0`B. `2/(sqrt(3))tan^(-1)(sqrt(3)((y^(2)-1)/(x^(2)-1)))-1/4 "In" (6((y^(2)-1)/(x^(2)-1))^(2)+2)-"In"sqrt(|x^(2)-1|)+tanc=0`C. `2/(sqrt(3))tan^(-1)(sqrt(3)((y^(2)-1)/(x^(2)-1)))-1/4 "In" (6((y^(2)-1)/(x^(2)-1))^(2)+2)-"In"sqrt(|x^(2)-1|)+e^(c)=0`D. `2/(sqrt(3))tan^(-1)(sqrt(3)((y^(2)-1)/(x^(2)-1)))-1/4 "In" (6((x^(2)-1)/(y^(2)-1))^(2)+2)-"In"sqrt(|x^(2)-1|)+e^(c)=0` |
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Answer» Correct Answer - A::B `(((x^(2)-1)+4(y^(2)-1))x)/((4(x^(2)-1)-3(y^(2)-1))y)=(dy)/(dx)` Let `y^(2)-1=v(x^(2)-1)` `implies (6v^(2)+2)/(4-3v)=((x^(2)-1)/x) (dv)/(dx)` `=int (4-3v)/(6v^(2)+2)dv = int x/ (x^(2)-1) dx` `implies2/(sqrt(3)) tan^(-1) (sqrt(3) ((y^(2)-1)/(x^(2)-1)))-1/4 "In" (6((y^(2)-1)/(x^(2)-1))^(2)+2)-"In" sqrt(|x^(2)-1|)+c=0` |
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