1.determine which functions are solutions of the linear differential equation.

y 6y + 9y = 0

2.find the Wronskian for the set of functions.

{x, e^x, e^x}

3.show that the set of solutions of a second-order linear homogeneous differential equation is linearly independent.

{e^ax, xe^ax}

4.verify that each solution satisfies the differential equation, (b) test the set of solutions for linear independence, and (c) if the set is linearly independent, then write the general solution of the differential equation.

y 4y + 5y = 0

5.perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.

5x2 2xy + 5y2 24 = 0

Larson, Ron (2016-01-01). Elementary Linear Algebra (Page 226). Brooks Cole. Kindle Edition.