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.