If y=f(x) is the solution of differential equation , e^y((dy)/(dx)-2)=e^(3x) such that f(0)=0 , then f(2) is equal to :

If y=f(x) is the solution of differential equation , e^y((dy)/(dx)-2)=

1.	If y=f(x) is the solution of differential equation , e^y((dy)/(dx)-2)=e^(3x) such that f(0)=0 , then f(2) is equal to :
Answer» 3 5 6 None of these Solution :Put `e^y =t rArr e^y DY= dtrArr (dt)/(dx)-2t=e^(3X)` I.F. =`e^(INT -2dx) =e^(-2x)` `t.e^(-2x) = int e^(3x). E^(-2x) dx` `t.e^(-2x) = inte^X dx= e^x +c , e^y e^(-2x) =e^x + c` Put x=0 ,y=0 we get `e^0 .e^0 =1+c` `rArr e^y e^(-2x)= e^x` `e^y =e^(3x) rArr y=3x rArr f(x)=3x`

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If y=f(x) is the solution of differential equation , e^y((dy)/(dx)-2)=e^(3x) such that f(0)=0 , then f(2) is equal to :

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