Verify that the indicated function y = (x) is an explicit solution of the given first-order differential equation. y? = 2xy^2; y = 1/(4 - x)^2 When y = 1/(4 - x)^2 Thus, in terms of x, 2xy^2 Since the left and right hand sides of the differential equation are equal when 1/(4 -x^2) is substituted for y, y = 1/(4 -x)^2 is a solution. Proceed as in Example 4 of Section 1.1; by considering simply as a function, give its domain. (Enter your answer using interval notation.) Then by considering as a solution of the differential equation, give at least one interval I of definition. Solution y = 1/(4 - x^2) y\' = -1/(4 - x^2)^2 * (-2x) y\' = 2x / (4 - x^2)^2 ---> first answer Thus, in terms of x, 2xy^2 = y\' 2xy^2 = 2x / (4 - x^2)^2 ---> second answer Here, phi(x) = 1/(4 - x^2) Denominator cnanot equal 0 4 - x^2 = 0 x^2 = 4 x = 2 , -2 So, x cannot be 2 or -2 So, domain ---> (-inf , -2) U (-2 , 2) U (2 , inf) ---> third answer Then by considering ....... (-2 , 2) ---> fourth answer.