Can you please help me with the differential equations problem below?

For problem #16 shown below, do the following:

1) Verify that the equilibrium point at the origin is a center by showing that the real parts of the system;s complex eigenvalues are zero [I GET THIS PART].

2) Calculate and sketch the vector generated by the right hand side of the system at the point (1,0). Use this to help sketch the elliptical solution trajectory for the system passing through the point (1,0). Draw arrows on the solution, indicating the direction of motion [WHAT SHOULD I DRAW EXACTLY IF I DIDN'T HAVE A NUMERICAL SOLVER HANDYjQuery22408762150756790585_1573157375922].

3) Use your numerical solver to check your result [I AM SUPPOSED TO USE SAGE; CAN YOU PLEASE HELP ME WITH THE CODE?]

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