(*______
2
σ
andrareparametersofaPartialDifferentialEquation______*)​​EQ=rXi[1][x,t]+rx
′
Xi[2]
[t]-
(0,1)
Xi[1]
[x,t]+
2
x
2
σ
(1,0)
f
[x,t]-rx
(1,0)
Xi[1]
[x,t]-
1
2
2
x
2
σ
(2,0)
Xi[1]
[x,t];
In[]:=
DSolve[EQ0,Xi[1][x,t],{x,t}]
Out[]=
DSolverXi[1][x,t]+rx
′
Xi[2]
[t]-
(0,1)
Xi[1]
[x,t]+
2
x
2
σ
(1,0)
f
[x,t]-rx
(1,0)
Xi[1]
[x,t]-
1
2
2
x
2
σ
(2,0)
Xi[1]
[x,t]0,Xi[1][x,t],{x,t}
In[]:=
DSolve[EQ0,f[x,t],{x,t}]
Out[]=
f[x,t]

1
[t]+
x
∫
1
-2rXi[1][K[1],t]-2rK[1]
′
Xi[2]
[t]+2
(0,1)
Xi[1]
[K[1],t]+2rK[1]
(1,0)
Xi[1]
[K[1],t]+
2
σ
2
K[1]
(2,0)
Xi[1]
[K[1],t]
2
2
σ
2
K[1]
K[1]
In[]:=
DSolve[EQ0,Xi[2][t],{t}]
Out[]=
Xi[2][t]

1
+
t
∫
1
-2rXi[1][x,K[1]]+2
(0,1)
Xi[1]
[x,K[1]]-2
2
x
2
σ
(1,0)
f
[x,K[1]]+2rx
(1,0)
Xi[1]
[x,K[1]]+
2
x
2
σ
(2,0)
Xi[1]
[x,K[1]]
2rx
K[1]