Exercises and Problems for Section 11.1 Exercises 8. A q 1. Is y = x3 a solution to the differential equation 2. Determine whether each function is a solution to the dit ,ferential equation and justify your answer: dr (a) (c) y=z4 y=x3 (b) (d) y=x4 + 3 y=7x4 9. Fil 3. Determine whether each function is a solution to the dif dy ter ferential equation and justify your answer:" 6r dx ^\ (a) y=4x3 (b) y=22,3/2 (c) y=623/2 4.. Show that y(x) = AeAz is a solution to the equation 10. Us y' = y for any value of A. on 5. Show that y = sin 2t satisfies 6 In Exe ential e dition. 11· 20 12. P dt2 6. Show that, for any constant R, the function P = Pet satisfies the equation d P 7. Use implicit differentiation to show that x2 + y2 r2 is 13. a solution to the differential equation dy/dr--/y. 14. Q Problems 15. Show that y = A + Cekt is a solution to the equation 18.