i need to find the extremal of the functional $\int I(y,y'') dt$. Could anyone tell me the concepts of finding the extremal so that i can go about solving this one?
Update:
So my function was: G= $\int(ay+ $$\frac{1}{2}$$ b$y''^2$ )dt$ solving it using using the Euler–Lagrange equation as given in the link below, we get:
a+by''''=0
which on solving gives:
y=-(a(t^4))/(24b).
Am i right in solving this one?