1. [1/2 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP10 1.1.001. 5. [-/4 Points] DETAILS ZILLDIFFEQMODAP10 1.1.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER State the order of the given ordinary differential equation verify that the Indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of for each solution. (1 - x) - 4xy' * By - cos x y" - 4y' + 20y - 0: P = ex cos 4x When y = 62x cos 4x, Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1. y' = a(x)+ an _ (x]+ ...+ (x)y + an ()+ 20(x) - (x) (6) linear nonlinear Thus, in terrns of x " - 4 + 20y - 2. [1/2 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP10 1,1.005. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 6. [-/4 Points] DETAILS ZILLDIFFEQMODAP10 1.1.017. State the order of the given ordinary differential equation. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER verify that the indicated function y = (x) is an explicit so is an explicit solution of the given first-order differential equation. y' = 2xyl; y = 1/(9 - x2) When y = 1/(9 - x2 ), Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1. an() + an-()_+ ...+ 2(x)0% + ag(x) - 9(x] (6) Thus, In terms of x, linear 2xy/2 - O nonlinear solution. Since the left and right hand sides of the differential equation are equal when 1/(9 - x2) is substituted for y, y - 1/(9 - x2) Proceed as in Example 4 of Se simply as a function, give its domain. (Enter your answer using inter. notation.) 3. [1/2 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP10 1,1.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Then by considering p as a solution of the differential equation, give at least one interval I of definition. O (0, 69) state the order of the given ordinary differential equation. O (-w, -3 (sin my* - (cos 8)' - 7 O (-BE, D) O (-3, 3) Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1. .. + 21(x)"2 + 20(x) - g(x) (6) O linear O nonlinear 7. [2/3 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP10 1.1.019. MY NOTES ASK YOUR TEACHER On your own, verify that the indicated expression is an implicit solution of the given first-order differential equation. n( zX - 1) = 4. [-/3 Points] DETAILS ZILLDIFFEQMODAP10 1.1.011. Which of the folowing is an explicit solution X - @((? MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER verity that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of OXEd definition for the solution. 2 - e When y = = */6 X = Thus, in terms of x. By'+ y = te xi Use a graphing utility to obtain the graph of the explicit solution chosen above. X