Find the variation of x(t)

Given differential equation

x''(t) + 7x'(t) + 5x(t) = 8u(t) where u is the unit step signal.

Initial Conditions: x(0) = 1, x'(0) = 2

Can someone please help me out to plot x(t) using Matlab with the given initial conditions?

Answer 1

[Chunru]

syms x(t)
Dx = diff(x, t);
eqn = diff(Dx, t) + 7* Dx + 5*x == 8

eqn(t) = 

cond = [x(0)==1, Dx(0)==2];
y = dsolve(eqn, cond)

y = 

fplot(y, [0 5])

[Abhinav Raghunandan]

Thank you so much for your response! I have a few queries regarding this:

does this take into consideration u(t) function as well where t>0?

and what is [0 5] in the fplot function?

[Chunru]

since u(t)=1 for t>0 and the initial condition is at t=0, it take cares of u(t).

[0, 5] indicates the plotting interval for t is from 0 to 5 as shown in the plot.

[Abhinav Raghunandan]

thank you so much!