Chapter 9.3, Problem 35E

a.

To determine

The solution of the linear differential equation $\frac{d^{2}x}{d{t}^2}+3\frac{dx}{dt}+2x=0$ with initial value’s $x(0)=1,x\text{'}(0)=0$ and sketch the graph of the solution.

b.

To determine

The solution of the linear differential equation $\frac{d^{2}x}{d{t}^2}+3\frac{dx}{dt}+2x=0$ with initial values $x(0)=1,x\text{'}(0)=-3$ , sketch the graph of the solution

c.

To determine

Qualitative difference of the solutions $x(t)=2e^{-2t}-e^{-t}$ and $x(t)=2e^{-t}-e^{-2t}$ with initial conditions $x(0)=1,x^{\text{'}}(0)=-3andx(0)=1,x^{\text{'}}(0)=0$ respectively of the linear differential equation $\frac{d^{2}x}{d{t}^2}+3\frac{dx}{dt}+2x=0$ and how many times will the oscillator go through the equilibrium state $x=0$ for each solution.