- #1
zak8000
- 74
- 0
hi
the differential equation i am attempting to solve is:
[tex] \frac {dP} {dx} = \frac {gP} {1+P/Psat} [/tex]
here is what I have done:
[tex] \frac {dP} {dx} = \frac {gP*Psat} {Psat+P} [/tex]
divide both sides by [tex] \frac {Psat+P} {gP*Psat} [/tex]
to get:
[tex] \frac {Psat+P} {P*Psat} \frac {dP} {dx} =g [/tex]
[tex]\int \frac {Psat+P} {P*Psat} dp = \int gdx [/tex]
[tex]\int \frac {dp} {P}+ \int \frac {dp} {Psat} =gx+c [/tex]
[tex]ln(P)+ \frac {P} {Psat} =gx+c [/tex]
now how do i rearrange P on one side with everything else on the other side
the differential equation i am attempting to solve is:
[tex] \frac {dP} {dx} = \frac {gP} {1+P/Psat} [/tex]
here is what I have done:
[tex] \frac {dP} {dx} = \frac {gP*Psat} {Psat+P} [/tex]
divide both sides by [tex] \frac {Psat+P} {gP*Psat} [/tex]
to get:
[tex] \frac {Psat+P} {P*Psat} \frac {dP} {dx} =g [/tex]
[tex]\int \frac {Psat+P} {P*Psat} dp = \int gdx [/tex]
[tex]\int \frac {dp} {P}+ \int \frac {dp} {Psat} =gx+c [/tex]
[tex]ln(P)+ \frac {P} {Psat} =gx+c [/tex]
now how do i rearrange P on one side with everything else on the other side