Given the second order non linear BVP

(')^n = 1 + γ θ .. 1

θ" + (λ +n+1/ 2n +1) θ' - n (2 λ +1/2n+ 1) * ' θ = 0 2

Prime in the above eqns describe partial differentiation with respect to η

Boundary conditions are

(0) = 0, θ'(0) = -1

' (∞) = 0, θ(∞) = 0

where η is a function of x & y given by

Similarity variable, η = x ^ (λ-n/2n+1) * y

Θ is a dimensionless temperature

is a dimensionless stream function given by

Stream function, ψ = x ^ (λ+n+1/2n+1) * (η)

how to solve the above system of PD eqns

the above system of equations are related to mixed convection of non newtonian fluids

n is the viscosity index

I haven't confused with n's and η's anywhere

I think that equations are differentiable with respect to η and η is function of x and y

So the equations are PDEs

Actually these equations are related to boundary layer mixed convection of non Newtonian fluids on vertical plate