(a) Use the fact that 5x? - y? = c is a one-parameter family of solutions of the differential equation y Y = 5x to find an implicit solution of the initial-value problem y oy = 5x, y(3) = -9. dx Then...

Extracted text: (a) Use the fact that 5x? - y? = c is a one-parameter family of solutions of the differential equation y Y = 5x to find an implicit solution of the initial-value problem y oy = 5x, y(3) = -9. dx Then sketch the graph of the explicit solution of this problem. y 20 20 10 10- (-9, 3) -20 -10 10 20 -20 -10 10 20 (3, -9) -10 10- - 20 -20 y 20- 20 10 10 (-9, 3) - 20 -10 10 20 -20 -10 10 20 (3, -9) 10 -10 -20 Give the interval I of definition of the explicit solution. (Enter your answer using interval notation.) (b) Are there any explicit solutions of y dy = 5x that pass through the origin? (If yes, enter the explicit solutions as a comma-separated list. If not, enter NONE.) y = 10