Question

2. -13 points ZillDiffEQModAp111.1.011. 0/6 Submissions Used My Notes Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate intervall of definition for the solution. 6y + y = 0; y = e-x/6 When y = e-x/6 y'a Thus, in terms of x, 6y' + y =

Answer 1

Sp" ingly yaeng. then y'= 44) =% Away They in terms of x, by ty = 0 + 46 . =10. Cansit Hence Y=ė N16 is an explicit solution of the differential equation Gylty=o. (Aus.) Louven Y= on is a one-parameter family of Solutions of the Ist order DE y'=Y-Y²-0 To find a solution of the IVP consisting of .: the given differential equation of the initial condition Y (o) = 1/2 , we use y (0) = £ in you ex ; . . then. f = t - 1+G=2 ; G = d. : the required solution is y=tex (Aus.) 244 Güven, yr amte is a one parameter family - of solutions of the Ist order D.E. Y'+2x4"=0-6. : To find a solution of the TVP Consisting of the given differential est ① & the initial condition y (3) = 1/6, we use Y (3) = 1/3 in j = h . then t = ate ²c=(4). . the required solution is y=-

Note that the solution exists if x²+ 4 . - ie. if x&#2 And also the interval of existence of solution must Contain the point 3. They the required largest intervalis, I=(2,00) over which solution is defined (Angly