Question

Consider the differential equation

Use the drop-down menus to answer to determine whether the following statements are TRUE or FALSE.

Question 2 7.5 / 10 pts Consider the differential equation y' + 3x~ y' + 6xy = 0. Use the drop-down menus to answer to determine whether the following statements are TRUE or FALSE. (1) y = -C3 = e is a solution of the differential equation for any constant c. False 3 (2) y = ce is a solution of the differential equation for any constant c. [Select] (3) y = = e-m3 is a solution of the differential equation and is the ONLY solution satisfying the initial conditions y(0) = 1, y(0) = 0. [Select] (4) There can be multiple functions that satisfy the differential equation and the initial conditions y(0) =1, 7(0) = 0. True Answer 1: False Answer 2: True Answer 3: True Answer 4: True

Answer 1

2) 7+32° 4'+607-6---) (1) y = 6 x baceca Now -ex y = - 3cx²ê 7 - 9 à ce 62 T + 3 x 4 + 6x4 ex aux excée gext to is not a solution of (A), for -ex3 3۔ tore -cx3 So, y = Constant e ceny C. FALSE (2) y = cex - J'=-3x²c ex y = -6x cet artcex Now Y"+3x²5'+6xy =-67/lett axlee x axtce & Excex So, y = cet is a solution of (A), for فر any Constant C. TRUE 23 70 = 1,760 - 0 such that y = -32 02 4x² 23 " 92 02 62 e 2 Now gr+ 32²y '+ 6 xy = 9x²0 2 - 6x6 ax xe x 9x62 70 so goed is not a sol of (A) FALSE terén