Use Laplace Transform to solve the initial value problem.
Please show all work and steps clearly so I can follow your
logic and learn to solve similar ones myself. I will also rate your
answer. Thank you kindly!
y′′ + 4y = f(t), y(0) = 0, y′(0) = 0,
where;
f(t)= 1 if 1 ≤ t < 2,
0 otherwise
Follow the steps bellow to construct a general solution to the
equation:
y'' + y = 3sect -t2+1
a. find the general solution to the homogeneous version of the
problem
b. find the particular solution to y'' + y = 3sect
c. find the particular solution to y'' + y =
-t2+1
d. use part (a), (b), (c) to construc the general solution to
the original given DE
Use a Laplace Transform technique to find the solution to the
differential equation (ie. initial value problem).
y'' + 4y' + 5y = 35e^(-4t)
y(0) = -3
y'(0) = 1
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation.
y''+2y'+5y=3sin(2t)
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation.
y''+4y=3csc2t
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation.
y''+2y'+y=2e^t