Solve `e^((dy)/(dx))=x+1,` given that when `x=0,y=3.`

Answer

`y=(x+1)(log_(e)(x+1))-x+3`

Explanation

`e^((dy)/(dx))=x+1`
or `(dy)(dx) = log(x+1)`
or `intdy=intlog(x+1)dx`
or `y=(x+1)log(x+1)-x+c`
when x=0, y=3 is c=3
Hence, the solution is `y=(x+1)log(x+1)-x+3`