Differential Equations

27. y'' + 25y = sin(4t), y(0) = 0, y'(0) = 0. Plot the component curves and the orbit, the latter for the rectangle |y|< 0.25 and |y'|< 1. Any surprises? 28. Hearts and Eyes: Find a solution formula for y'' + 25y = sin&(wt), where w is not equal 5. Plot the solution curve of the IVP with y(0) = y'(0), where w=4. Plot the orbit for 0< t <20 in the rectangle |y| < 0.1, -0.5 < |y'| < 0.3. Repeat with w=1. Overlay the graphs.

Initial Value Problem - Unique Solution?

Determine whether the given initial value problem has a unique solution (using Theorem 1) *Please see attachment for problem (Direct "yes/no" answer is fine)

Asymptotic Behavior of Solution

Use the phase line to predict the asymptotic (*see attachment*) behavior of the solution satisfying the specified initial condition ... *Please see attachment for complete question.

Find a second Linearly independent solution

see file attached

Determine inertia, damping, and stiffness using given data

see attached file