Thread: finding an extremal

If , show that the extremal is

I've done:




Then using Euler's equation we get:



So

and then I'm stuck from here, I can't see how to turn this is into trigonometric functions? I tried letting which didn't work...

Can anyone please help me?

Thanks in advance!

Solve the differential equation 1- y"= y which is the same as y"+ y= 1. That's a linear equation with constant coefficients. Its characteristic equation is and I recommend trying y= A, a constant, for the "specific solution".

This problem clearly expects you to be able to solve that differential equation.