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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

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# Solving a first order differential equation

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