Solve the differential equation y'' − y' − 2y = 9e^2t , with
initial conditions y(0) = 3, y' (0) = −2, using two different
methods. Indicate clearly which methods you are using. First
method:
Second method:
Given the differential equation
y''+y'+2y=0, y(0)=−1, y'(0)=2y′′+y′+2y=0, y(0)=-1, y′(0)=2
Apply the Laplace Transform and solve for Y(s)=L{y}Y(s)=L{y}. You
do not need to actually find the solution to the differential
equation.
3. Consider4 the homogenous linear second order differential
equation
y′′ − 2y′ + y = 0 (⋆)
(a) Verify that the function y = e^x is a solution of equation
(⋆) on the interval (−∞, ∞).
(b) Verify that the function y = xex is a solution of equation
(⋆) on the interval (−∞, ∞).
(c) Verify that y = 7e^x + (5xe)^x is a solution of equation
(⋆) on the interval (−∞, ∞).
(d) Assume that c and d...