Please see the attached file for the fully formatted problem.
Solve the IVP:
y'' + 4y' +13y = 13t2 -5t +24 +e^-2t(sin 3t)
Please see the attached file for the complete solution.
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Step 1: Find the general solution to the homogenous problem where the RHS is 0.
Let . Then . This has roots . This gives the solution .
Step 2: Find a particular solution to the full problem by using suitable "guesses".
In this case, the guess will look like:
(Note: we need the "t" in front of the last term because the solution to the homogenous ...
The expert examines initial value problems solved.
Encompassing initial value problems
Solve the initial value problems;
1a) t(dy/dt) + 5y = 7t w/ y(1) = 3
1b) (dy/dt) + 0.1ty = 7t w/ y(0) = 4
1c) 11(t+1)(dy/dt) - 7y = 28t for t > -1 w/ y(0) = 20
1d) (dy/dt) + 2y = 25sin(t) + 30cos(t) y(0) = 1
1e) (dy/dt) + 5y = cos(4t) w/ y(0) = 0
1f) 9(dy/dt) + y = 18t w/ y(0) = 1 find y as a function of t
1g) Find the function satisfying the differential equation
f'(t) - f(t) = 4t w/ f(1) = -1
1h) Find the particular solution of the differential equation
(dy/dx) + ycos(x) = 6cos(x) w/ y(0) = 8