Black-Scholes PDE and finding the general solution

1. Apr 8, 2012

meghibbert17

Hello, I have the PDE

$\frac{-∂v}{∂τ}$+$\frac{1}{2}$σ$^{2}$ε$^{2}$$\frac{∂^{2}v}{∂ε^{2}}$+($\frac{1}{T}$+(r-D)ε)$\frac{∂v}{∂ε}$=0

and firstly I need to seek a solution of the form v=α$_{1}$(τ)ε + α$_{0}$(τ) and then determine the general solution for α$_{1}$(τ) and α$_{0}$(τ).

I am given that ε=$\frac{I}{TS}$ - $\frac{X}{S}$ and that τ=T-t.

Can anybody help me with this problem?

Thankyou

2. Apr 8, 2012

chiro

Hey meghibbert17 and welcome to the forums.

Are you familiar with the idea for transforming the B.S. to a standard PDE heat equation?