This is an optimal control problem for an econ class but it is the maths behind it I am struggling with - so have left the context out. I have derived two differential equations in my state and costate variables:
where is some arbitrary constant.
Now i need to solve for
Using the integrating factor I get:
Where is another arbitrary constant. Is this right?
I then have to apply the transversality condition:
Which using my solutions for and is:
I won't go any further with the problem here because I am convinced I have gone wrong somewhere since the equation isn't very pretty can anyone check my value for please?