Green's Function I-Mathematical Physics-Assignment, Exercises of Mathematical Physics

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- = \ Mathematical Methods — | Assignment Number 2. PAM -507 (Due on February 10, 2011) Question 1. Use the Green’s function method to solve the following initial value problems (a) y'-y=1 y(0)=0 y(0)=1 (b) y" -3y/ -4y =e | y(2)=3 y(2)=1 (c) ty" +ty’+4y= sin (log t) y(1)=1 y(1)=0 (d) y" ty’ = 8(t-n)- 8(t-27) y0)=1 y(O)=1 (e) y+ y= 58(t-n/2)sin (t) y(0)=0 y(0)=2 Question 2. Construct the Green’s function, if possible, for the following operator and boundary conditions (where D== ) (a) L =D’ y(a)=0 and y(b)=0 “st (b) L=D? y(0)=0 y(1)=0 (c) L= x? D?+2xD +1 y(1)=0 y(e")=0 Question 3 Show that the Green’s function of the following ODE does not exist yitmwy=mx y(0)=1 y(i)=0 Then find the solution. Question 4 Use Green’s function method to find the particular solution of the following ODE yo-y=x : y(0)=0 y(1)=0 docsity.com