Block Diagram - $x(t)$ and $y(t)$, but $y(t)$ does not exist, only $y'(t)$

Question

I have the transfer function: $$H\left(s\right)=\frac{s+50}{s\left(s+1\right)\left(s+3\right)}=\frac{Y\left(s\right)}{X\left(s\right)}$$ and: $$H_1\left(s\right)=\frac{1}{s\left(s+1\right)\left(s+3\right)}$$ If I am trying to get to the ODE, I receive: $$x(t)=y'''\left(t\right)+4y''\left(t\right)+3y'\left(t\right)$$ Since I dont have an output $y(t)$, how do I paint the block diagram?
is it okay if my output is y'(t)? if I define $h(t)=y'(t)$ and thus I have $h(t)$ as output? or it is no good?