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Initial-Value Problem Solved

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

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https://brainmass.com/math/numerical-analysis/initial-value-problem-solved-211707

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Solve

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.

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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

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