Find the general solution to the driven differential equation

Show how you would have done things by hand. Find the general solution to the driven differential equation attached.

Find the solution to the attached

Show how you would have done things by hand. Find the solution to the attached.

Consider the differential equation attached

Show how you would have done things by hand. Consider the differential equation attached. The graph is shown. a) Is this differential equation linear or nonlinear? Is it autonomous or nonautonomous? b) Without solving, use the graph to determine the limiting value... (see attached for rest).

Use variation of parameters

Show how you would have done things by hand. One solution of the equation attached is y(t) = t. Find the general solution. Use variation of parameters to find a particular solution of the equation attached.

Differential Equation: Continuous Functions; Fundamental Set of Solutions; Coefficient Functions

Consider the attached differential equation where I = (a,b) and p,q are continuous functions on I. (a) Prove that if y1 and y2 both have a maximum at the same point in I, then they can not be a fundamental set of solutions for the attached equation. (b) Let I = {see attachment}. Is {cos t, cos 2t} a fundamental set of solutions for the attached equation for some p(t),q(t)? If no, why not? If yes, what are the coefficient functions p(t) and q(t)? NOTE: No computer, no calculator. Show how you would have done things by hand. Thanks so much!