$y=0$ is singular solution of $\frac{dy}{dx}=E(y)$ iff the improper integral $\int_{0}^{1}\frac{dy}{E(y)}$ is convergent

Question

Assume that a continuous function $E(y)$ is such that $$E(0)=0,~~~~E(y)\neq 0,~~~~0<y\le 1.$$ Then $y=0$ is the singular solution of the differential equation $$ \dfrac{dy}{dx}=E(y), $$ if and only if the improper integral $$ \int_{0}^{1}\dfrac{dy}{E(y)}$$ is convergent.

This problem is from china ODE problem (can see :http://item.jd.com/1048628556.html, page 111. problem 4, and I don't see any book have solution by this problem. Thank you