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If y=f(x) is the solution of differentia...

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 :

A

3

B

5

C

6

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Put `e^y =t rArr e^y dy = dt rArr (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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