7. [-3 Points] DETAILS ZILLDIFFEQMODAP11 2.3.017. MY NOTES ASK YOUR TEACHER Find the general solution of the given differential equation. cos(x) E + (sin(x))y = 1 dx eel l Give the largest interval over which the general solution is dened. (Think about the implications of any' singular points.) 0011) 2 O (,1, 1) O (0. '1') O (.00, no) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a commaseparated list; if there are none, enter NONE.) Z Need Help? 8. [-3 Points] DETAILS ZILLDIFFEQMODAP11 2.3.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the general solution of the given differential equation. +2rp=p+sr4 dt Give the largest interval over which the general solution is dened. (Think about the implications of any singular points. Enter your answer using interval notation.) E Determine whether there are any transient terms in the general solution. (Enter the transient terms as a commaseparated list; if there are none, enter NONE.) : Need Help? 9. [-12 Points] DETAILS ZILLDIFFEQMODAP11 2.3.025.Ml. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Solve the given initial-value problem. =x+7y, y(0)=2 dx W) = I I Give the largest interval I over which the solution is defined. (Enter your answer using interval notation.) Need Help? 10. [-12 Points] DETAILS ZILLDIFFEQMODAP11 2.5.027. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Solve the given initial-value problem. Xv'+y=e". y(1)=7 Give the largest interval I over which the solution is defined. (Enter your answer using interval notation.) V00 = I: Need Help? 11. [-5 Points] DETAILS ZILLDIFFEQMDDAPH 2.3.038.EP. | MY NOTES I | ASK YOUR TEACHER I PRACTICE ANOTHER I Consider the following differential equation. % + Y = x), y(0) = 1, where f(x) ={ x 1, 03x31 1, x>1 Find the coefcient function P(x) when the given differential equation is written in the standard form % + P(x)y = x). X P(x) = Find the integrating factor for the differential equation. Proceed as in Example 6 in Section 2.3 to solve the given initialvalue problem. ,osxs1 ix>1 V\") = Use a graphing utility to graph the continuous function y(x). 5. [-15 Points] DETAILS ZILLDIFFEQMODAP11 2.3.009.EP. MY NOTES ASK YOUR TEACHER Consider the following differential equation. x3 y = x2 sin(x) dx Find the coefcient function P(x) when the given differential equation is written in the standard form % + P(x)y = fix). x Find the integrating factor for the dlfferential equation. 91m) dx = Find the general solution of the given differential equation. P(x) = V00 = Give the largest interval over which the general solution is dened. (Think about the implications of any singular points. Enter your answer using interval notation.) E Determine whether there are any transient terms in the general solution. (Enter the transient terms as a commaseparated list; if there are noner enter NONE.) : Need Help? 6. [-15 Points] DETAILS ZILLDIFFEQMODAP11 2.3.015.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following differential equation. ydx 5(x + 1/7) dy= 0 Find the coefcient function P(y) when the given differential equation is written in the standard form 3 + P(y)x = y). \"'9' Find the integrating factor for the differential equation. 81PM dy = Find the general solution of the given differential equation. PM = XU') = Give the largest interval I over which the general solution is dened. (Think about the implications of any singular points. Enter your answer using interval notation.) : Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.) : Need Help? 3. [-112 Points] DETAILS ZILLDIFFEQMODAP11 2.3.008.MI.SA. MY NOTES ASK YOURTEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find the general solution of the given differential equation. y' = 2:1 + x2 + 3 Give the largest interval over which the general solution is defined. Determine whether there are any transient terms in the general solution. Recall that the standard form of a linear rst-order differential equation is as follows. cl " + P