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.
