MA3475 -HW2 -Solved

1.    (5 points)  .

2.    (5 points)  .

3.    (5 points)  

  Extra problems for practice. No need to turn in. May involve hyperbolic functions.

b

1.       J[y] =y(x)2 + y(x)y′(x) + (y′(x))2 dx.

a

b

2.       J[y] =(1 + x)(y′(x))2 dx.

a

3.       Let p(x),q(x) be positive continuous functions defined on [a,b]. Let

 

where y(x) ∈ C2[a,b], y(a) = A,y(b) = B. Describe the Euler-Lagrange equation for this functional.