I don't know if your question was my problem, but when I want to DELAY THE RESPONSE, for example, when the voltage source pulse starts in tdelay = 0, the response, for example, the voltage starts in zero. BUT if the the voltage source pulse starts in tdelay = 3s, I can to force delay the response too, using the function "step unit" like the singular function using in the theory part. You must to write to plot u(time), the response in the transient simulation will be a the step unit. If you write to plot 3*u(time), the response in the transient simulation will be a the step unit multiplied by 3 and so on.
Now, if you write to plot 3*u(time-3), the response in the transient simulation will be a the step unit multiplied by 3, DELAYED so far 3 secs, that is to say, you can use the singular function of step unit in the simulator in the same way that you use in a theoretical part. See the attached pic. Observe that the Vpulse source its 3 seconds delayed and the simulator response (capacitor voltage, V(n002,n003), blue trace). I wrote the following equation and plot it (green trace), that is the theoretical response:
$$\frac{143}{7}u(3-time) + \left(\frac{173}{7}-\frac{30}{7}e^{-\frac{56}{17}(time-3)}\right)u(time-3)$$
Observe that the first part \$\frac{143}{7}u(3-time)\$ its the initial voltage in the capacitor, and the "down pick" in green trace in 3 secs its for this part of equation, because in t=3s, it has a discontinuity (speaking mathematically).
transient delayed analysis
