If `y=f(x)` is the solution of equation `ydx+dy=-e^(x)y^(2)`dy, f(0)=1 and area bounded by the curve `y=f(x), y=e^(x)` and x=1 is A, thenA. curve y=f(x) is passing through `(-2,e)`.B. Curve `y=f(x)` is passing through `(1,1//e)`C. curve `y=f(x)` is passing through `(1,1//3)`D. `A=e+2/sqrt(e )-3`

If `y=f(x)` is the solution of equation `ydx+dy=-e^(x)y^(2)`dy, f(0)=1

1.	If `y=f(x)` is the solution of equation `ydx+dy=-e^(x)y^(2)`dy, f(0)=1 and area bounded by the curve `y=f(x), y=e^(x)` and x=1 is A, thenA. curve y=f(x) is passing through `(-2,e)`.B. Curve `y=f(x)` is passing through `(1,1//e)`C. curve `y=f(x)` is passing through `(1,1//3)`D. `A=e+2/sqrt(e )-3`
Answer» Correct Answer - A::D `ydx+dy=-e^(x)y^(2)dy` `rArr (e^(-x)ydx+e^(-x)dy)/(y^(2))=-dy` `rArr d(e^(-x)/y)=dy` `rArr e^(-x)=y^(2)+cy` `therefore f(0)=1, therefore c=0` `rArr e^(-x)=y^(2)` `rArr y=e^(-x//2)` `rArr A = int_(0)^(1)(e^(x)-e^(-x//2))dx=e+2/sqrt(e)-3`

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If `y=f(x)` is the solution of equation `ydx+dy=-e^(x)y^(2)`dy, f(0)=1 and area bounded by the curve `y=f(x), y=e^(x)` and x=1 is A, thenA. curve y=f(x) is passing through `(-2,e)`.B. Curve `y=f(x)` is passing through `(1,1//e)`C. curve `y=f(x)` is passing through `(1,1//3)`D. `A=e+2/sqrt(e )-3`

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