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_____
1. Solve the third-order initial value problem below using the
method of Laplace transforms.
60y′′′+8y′′+11y′−20y=−60, y(0)=11, y′(0)=−10, y"(0)= 50
2. Use the method of Laplace transforms to find a general
solution to the differential equation below by assuming that a and
b are arbitrary constants.
5y′′+6y′+25y=5, y(0)=a, y'(0)=b
Find the general solution using REDUCTION OF ORDER. and
the Ansatz of the form y=uy1 = y=ue-x
(2x+1)y'' -2y' - (2x+3)y = (2x+1)2 ; y1 =
e-x
Thank you in advance