Solving for Integral with Partial Differentiation

[Economist2008]

Do you guys know if it's possible to solve for the following integral

l(t)=∫ {a+ [b+cL(t)+exp^L(t)]/d } dt

where a, b, c and d are constants and the derivative of L(t) is l(t).

Thanks in advance!

 

[Defennder]

If you differentiate both sides, you get a DE of the form:
L'' = f(L).

You have by the chain rule:
d^2 L /dt = (dL/dt) d/dL (dL/dt) and
L'' = L' d/dL (L') = d/dL 1/2 (L')^2 = f(L) which is separable.

EDIT: Why does your thread read "partial differentiation"?