$-u''+u=\delta_y$ where $u(0)=u(1)=0$

Question

Let $0<y<1$ be arbitrary. What is the weak solution of the differential equation

$-u''+u=\delta_y$ where $u(0)=u(1)=0$

then? The weak form of the equation above is given by

$\int_0^1{u'(t)v'(t)+u(t)v(t)dt}=v(y)$ for all $v\in H_0^1((0, 1))$.