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 t ...continues

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

Find Critical Point Set for the given system

Find the critical point set for the given system .... *Please see attachment for system

Elimination Method to Solve Linear System

Use elimination method to find a general solution to the given linear system, where differentiation is with respect to t. *(Please see attachment for linear system)

Determine the first three non-zero terms in Taylor polynomial appximations

see attached file

Inhomogeneous Differential Equations / Initial Value Problems

Please typeset your solution. 1. Find the general solution to these inhomogeneous differential equations: (see attachment) 2. Solve the following initial value problems (see attachment)

Variation of Parameters

1. Find the general solution of 1. x^2*f" + x*f - f = x' 2. y" + 9y = sec^2(3t) using the method of variation of parameters . Thanks.