The solution of `e^(dy//dx) = (x+1) , y (0) = 3 ` is

Options

A. `y = (x+1) log |x+1| - x+3`
B. ` y = (x+1) log |x +1| + x +3`
C. ` y = (x +1) log |x+1| + x + 3 `
D. ` y = log x + x +3`

Answer

b

Explanation

Given , ` (dy)/(dx) = log(x+1)`
` rArr dy = log (x+1) dx`
` rArr int dy= int log ( x+1) dx `
` rArr y = (x+1) log |x =1| - x +C`
` :. X = 0, y = 3`
` :. C = 3`
` :. Y = (x+1) log | x+1| - x+3`