Explore BrainMass

Initial-Value Problem Solved

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Please see the attached file for the fully formatted problem.

Solve the IVP:
y'' + 4y' +13y = 13t2 -5t +24 +e^-2t(sin 3t)

© BrainMass Inc. brainmass.com October 24, 2018, 11:57 pm ad1c9bdddf


Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.


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 ...

Solution Summary

The expert examines initial value problems solved.

See Also This Related BrainMass Solution

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

View Full Posting Details