Calculus of Variations: Find extremal of functional I[y(x)] = ∫(e-x·y′² - ex·y2)dx
I've been given a problem that goes like this,
Find the extremal of the functional:
I[y(x)] = ∫(e-x·y′² - ex·y2)dx, limits being 0 to ln 2
If Euler's theorem is to be followed, I computed the condition:((∂f/∂y) - d(∂f/∂y′)/dx) = 0
to be: -y″ + y′ + e2x·y = 0
However, I am not able to solve the DE any further. Please guide me.
I've been given a problem that goes like this,
Find the extremal of the functional:
I[y(x)] = ∫(e-x·y′² - ex·y2)dx, limits being 0 to ln 2
If Euler's theorem is to be followed, I computed the condition:((∂f/∂y) - d(∂f/∂y′)/dx) = 0
to be: -y″ + y′ + e2x·y = 0
However, I am not able to solve the DE any further. Please guide me.