Thread: Differentiation Crisis

Hi I'm stuck with a problem, I'm fine with differentials but the way this is worded confuses me!

Valuation of a storage facility gives equation:

V'' - rV = cP where c and r are constants

V: R->R is a function of the variable P and it wants me to find the general solution V (P).

I'm going round in circles here, if V is a function of P then am I right in saying V'' = d^2V/dP^2 ??
but then where do I go, do they want V = P something?

please help!

Originally Posted by mathgrad

Hi I'm stuck with a problem, I'm fine with differentials but the way this is worded confuses me!

Valuation of a storage facility gives equation:

V'' - rV = cP where c and r are constants

V: R->R is a function of the variable P and it wants me to find the general solution V (P).

I'm going round in circles here, if V is a function of P then am I right in saying V'' = d^2V/dP^2 ??
but then where do I go, do they want V = P something?

please help!

This is a standard second order linear ordinary differential equation.

We first look for the general solution of:



For this take a trial solution , then as:



we have:



so if



and so

So the general solution to is:



where and are arbitary constants.

Now to get the general solution to we take any solution of this equation and add on the right hand side of above. An obvious solution is V(P)=cP, so the general solution is:



RonL