Let x and y be functions of t. Find the general solution of the system of equations below by first converting the system into second-order differential equations involving only x and y. Find a particular solution for the initial conditions. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system:
x' = y, y' = 20x - y; x(0) = 5, y(0) = -7
Solve for x(t). Choose the correct answer below:
A) x(t) = Ae^{-5t} + Be^{-5t}
B) x(t) = Ae^{4t} + Be^{-5t}
C) x(t) = A cos(-5t) + B sin(-5t)
D) x(t) = Ae^{-5t} + Bte^{-5t}
Now find y(t) so that y(t) and the solution for x(t) found in the previous step are a general solution to the system of differential equations.
y(t) =
Find a particular solution given the initial conditions x(0) = 5, y(0) = -7.
x(t) =
y(t) =
Use a computer system or graphing calculator to construct a direction field and typical solution curves for the system. Select the correct graph below: