[SOLVED] MA3475 -HW2

Description

Show your work as supported answers may receive no credit. Find the extremals of the following functionals.

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.