given the 3rd order differential equation: y''' - 3y'' + 2y' =
ex / (1 + e-x)
i) set u = y' to reduce the order of the equation to order 2
ii) solve the reduced equation using variation of parameters
iii) find the solution of the original differential equation
Consider the differential equation
y '' −
2y ' + 10y =
0; ex
cos(3x),
ex
sin(3x), (−∞, ∞).
Verify that the given functions form a fundamental set of
solutions of the differential equation on the indicated
interval.
The functions satisfy the differential equation and are linearly
independent since
W(ex
cos(3x),
ex
sin(3x)) = _____ANSWER HERE______ ≠ 0 for −∞ <
x < ∞.
Form the general solution.
y = ____ANSWER HERE_____
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: