Think about taking a small step, deltax, away from zero. If y(0) = 1 then dy/dx is non zero at x=0 and will start to change the value of y. However, if y(0) = 0, then day/dx is zero and hence is unable to give rise to a change in y, so at deltax the value of y is still zero. Repeating this for another step of deltax therefore still doesn't lead to a change in y. y stays at zero for all x.