Question

(a) Use the fact that 5x2 − y2 = c is a one-parameter family of solutions of the differential equation y dy/dx = 5x to find an implicit solution of the initial-value problem y dy/dx = 5x, y(4) = −10.

Then sketch the graph of the explicit solution of this problem.

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/dx = 5x  that pass through the origin? (If yes, enter the explicit solutions as a comma-separated list. If not, enter NONE.)

y =

Answer 1