Problem
In the solution for a two-dimensional laminar jet, the following nonlinear ordinary differential equation arises
where primes denote differentiation with respect to the independent variable η. The problem has the conditions 
and 
and the constraint
and and the constraint 
where a is a constant.
Write a function to solve this problem—that is, return values of f at specified values of η. The test suite allows MATLAB’s functions for numerical solution of ODEs, but the equation has a relatively simple analytical solution. If you would like a hint for the analytical solution, execute this command:
char('Zxj%ymj%uwtizhy%wzqj%tk%inkkjwjsynfynts%y|t%ynrjx%fsi%nsyjlwfyj%ymwjj%ynrjx3'-5)
Background
The physical problem involves a jet in the 
plane emanating from a source at 
. It can be solved by expressing the velocities u and v in terms of a streamfunction and employing a similarity solution that combines the spatial coordinates into a single variable η. In the problem above, 
is proportional to the streamfunction. The conditions at 
define the line 
as a line of symmetry; the transverse velocity v and the shear stress are zero there. The condition states that the streamwise velocity u is zero far from the source. The integral constraint states that the momentum flux of the jet is constant. The value 
corresponds to the physical problem of the jet. Other values are included for variety.
plane emanating from a source at . It can be solved by expressing the velocities u and v in terms of a streamfunction and employing a similarity solution that combines the spatial coordinates into a single variable η. In the problem above, is proportional to the streamfunction. The conditions at define the line as a line of symmetry; the transverse velocity v and the shear stress are zero there. The condition states that the streamwise velocity u is zero far from the source. The integral constraint states that the momentum flux of the jet is constant. The value corresponds to the physical problem of the jet. Other values are included for variety.Solution Stats
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The constraint that involves the constant 'a' is missing in the problem description.
Thanks for pointing out my omission.