Laplace II: Steps, Impulses & Convolution · Challenge problem

A tank at rest obeys $y'+y=u(t)-u(t-T)$, $y(0)=0$: a unit inflow runs from $t=0$ to $t=T$ and is then shut off. There is exactly one $T>0$ with $y(2T)=\dfrac14$. Find it.