In solving Exercises, recall that the principal value arcsin x of the inverse sine functio...

In solving Exercises, recall that the principal value arcsin x of the inverse sine function is restricted as follows:  ≤ arcsin x ≤ Refer to different arc segments in Figure which shows the graph of the ellipse .

Figure

Show that after the answers to Exercises 1 and 2 have been deleted, the remaining arcs of the ellipse  are not solutions of the differential equation

For this purpose consider the sign of the slope of the curve.

Exercises 1

In solving Exercises, recall that the principal value arcsin x of the inverse sine function is restricted as follows:  ≤ arcsin x ≤ Refer to different arc segments in Figure which shows the graph of the ellipse .

Figure

Solve the equation of Exercise with the added condition that whenx  = 0, .

Exercise

In solving Exercises, recall that the principal value arcsin x of the inverse sine function is restricted as follows:  ≤ arcsin x ≤

Exercises 2

In solving Exercises, recall that the principal value arcsin x of the inverse sine function is restricted as follows:  ≤ arcsin x ≤ Refer to different arc segments in Figure which shows the graph of the ellipse .

Figure

Solve the equation of Exercise with the added condition that when x  = 0, .

Exercise

In solving Exercises, recall that the principal value arcsin x of the inverse sine function is restricted as follows:  ≤ arcsin x ≤