I have to solve the integral equation $\displaystyle y(x)=1+2\int_0^x(t+y(t))dt, y_0(x)=1$ by the

method of successive approximation. Using $\displaystyle y_n(x)=1+x^2+2\int_0^x y_{n-1}(t)dt$, I can find $\displaystyle y_1(x), y_2(x), $ etc

but I cannot find any general expression for $\displaystyle y_n(x)$ and hence cant find the solution $\displaystyle y(x)(=\mbox{Lim} y_n(x))$ . Please help