1. [-/2 Points] DETAILS ZILLDIFFEQMODAP10 4.10.003. MY NOTES ASK YOUR TEACHER Solve the given differential equation by using the substitution u = y'. [Use x as the indepen "+ 072 + 1 =0 -10 -10 (b) Find an interval of definition for the solution in part (a). (Enter your answer using interval notation.) 2. [-/2 Points] DETAILS ZILLDIFFEQMODAP10 4.10.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Submit Answer Solve the given differential equation by using the su titution u = y'. (Use x as the ind . [-/2 Points] DETAILS ZILLDIFFEQMODAP10 4.10.013. MY NOTES ASK YOUR TEACHER Show that the substitution u = y' leads to a Bernoulli equation. equation (see Section 2.5). 3. [-/2 Points] DETAILS ZILLDIFFEQMODAP10 4.10.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Solve the given initial-value problem. (Use x as the independent variable.) 6. [-/3 Points] DETAILS ZILLDIFFEOMODAP10 4.10.015. 2y'" = 1, M(0) = 8. (0) = 1 MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Proceed as in Example 3 of Section 4.10 and obtain the first six nonzero terms lution, centered at 0, of the given initial-value problem. y" =x+ y'. (0) = 1. (0) = 1 4. [-/3 Points] DETAILS ZILLDIFFEQMODAP10 4.10.011. MY NOTES ASK YOUR TEACHER Consider the initial-value problem Use a numerical solve the solution curve with the graph of the Taylor polynomial. " + ry' - 0, >(0) = 1, v10) = =1. (a) Find an explicit solution of the IVP. (Use x as the independent variable.) Taylor polynomial Taylor polynomda Use a graphing utility to graph this solution, Taylor polynom an 85 10 13 20 25 -10 101 . [-/3 Points] DETAILS ZILLDIFFEQMODAP10 4.10.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Proceed as in Example 3 in Section 4.10 and obtain the first six nonzero terms of a Taylor series solution, centered at 0, of the given initial-value problem. = x + y - 4y'. >(0) = 1, y(0) = 1