On the Darboux integrability of Blasius and Falkner-Skan equation

We study the Darboux integrability of the celebrated Falkner-Skan equation f‴+ff″+λ(1-f′2)=0, where λ is a parameter. When λ = 0 this equation is known as Blasius equation. We show that both differential systems have no first integrals of Darboux type. Additionally we compute all the Darboux polynomials and all the exponential factors of these differential equations.