Question

a hint to find integral factor of SDE equation

Answer 1

\[dX _{t}=(1-X _{t})X _{t}dB _{t}\\\]
with B Brownian motion

Answer 2

my example

Given the Differential Equation (DE) (pxy2+qy)dx+(qx2y+px)dy=0,

a) Show that DE is exact if p=q.

b) Hence or otherwise, solve the DE if p=q=2.

c) If p≠q, find an integrating factor in the form of xrys, where r=f1(p,q) , s=f2(p,q). In other words, r and s are functions that can be expressed in terms of p and q.
d) Hence or otherwise, solve the DE if p=2, q=3. Express your answer in the form of xayb−xcyd=w where a,b,c,d∈Q and w is an arbitrary constant.

Answer 3

thank u but it works for ode
but it is an unusual stochastic diff equation !