How to calculate step response of an differential equation SYMBOLICALLY?

Hello,

I have a differential equation as follows:

Here the C_2 is output and C_i is input.

I have to calculate a step response SYMBOLICALLY from this system described by the equation. I'm able to do this with step(transfer function) but this time I want to calculate is symbolically.

Here's what I've made:

syms y t u 
syms y(t)

 % For prettier results I mark: C_1 = y & C_i = u
 % equ = equation in time domain:
 equ = (diff(diff(y,t),t))+(7*diff(y,t))+10*y-10*u;

 % Let's laplace transform the equation:
 EQU = laplace(equ,t,s)

 % Calculate step response by multiplying with (1/s) in s-domain:
 EQU_step = EQU*(1/s)

 % inverse transform:
 equ = ilaplace(EQU,s,t)

How ever I have a feeling that there must be more elegant way to do this symbolically. Furthermore I'm not sure if my code is working correctly. Have I done right?

Important part: How do I plot the result in time domain in order to compare the results with the figure that I've got with built-in function: step(transfer function object)?

Thank you of any kind of help!