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i'm willling to solve partial differential equation of the form:

dy/dt = d2y/dx2 + 2/x * dy/dx - 4y

where d here means partial derivation of course.

boundary conditions are: dy/dx(0,t) = 0, y(1,t) = 1, t>0

initial condition is: y(x,0) = 0;

(x,y) is position and t is time.

and t should be also chosen so as the solution doesn't differ from the stationary solution more than 5%, where the stationary solution is the one who is independent on time t.

Can you please give me some hints on how to start or think about this problem? I need to build some code to solve this equation using matlab.

Thank you. I'm looking forward to your answers.