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How to find P(x,y) with diff

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esat gulhan
esat gulhan on 9 Sep 2020
Commented: Alan Stevens on 9 Sep 2020
I am trying to solve this diff equation
u=a*x+b
v=-a*y+c*x
p=1
-dP/dy=(u*dv/dx+v*dv/dy)*p
-dP/dx=(u*du/dx+v*du/dy)*p
I want to find P(x,y) but i can not find
My code is below and i think it is absolutely wrong
syms a b c u v w x y z p Py(y) Px(x)
u=a*x+b
v=-a*y+c*x
eq=p*(u*diff(v,x)+v*diff(v,y))==-diff(Py,y)
Py(y)=dsolve(eq)
eq2=p*(u*diff(u,x)+v*diff(u,y))==-diff(Px,x)
Px(x)=dsolve(eq2)

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esat gulhan
esat gulhan on 9 Sep 2020
You are right but it does not find P(x,y) . I want to find the real P(x,y) without C1
Alan Stevens
Alan Stevens on 9 Sep 2020
To find P(x,y) without an arbitrary constant you need a boundary/initial condition e.g. P(0,0) = something.

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