Help solving a Differential equation

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SUMMARY

The discussion centers on solving the ordinary differential equation (ODE) y' = y^{-1/k} using MATLAB, resulting in the solution (t*k + t + C1*k)^{k/(1+k)}. The user successfully solved the ODE by hand, arriving at y^{(k+1)/k} = kt. Additionally, the user inquires about the applicability of Alternating Direction Implicit (ADI) Methods for solving heat equations in cylindrical coordinate systems.

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real10
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k is an integer greater than 1.
[tex]y'=y^{\frac{-1}{k}}[/tex]
solving this ode in MATLAB gives me this
[tex](\frac{t*k+t+C1*k}{k})^{\frac{k}{1+k}}[/tex] which is correct since the further part of the problem proving a certain limit involving y follows from using the above MATLAB sol.

I am interested in solving this ode by hand.

by hand I am getting [tex]y^{\frac{k+1}{k}}=kt[/tex]
 
Last edited:
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never mind I have solved it:smile:
 
I have a problem in heat equation. Can ADI Methods be used in Cylindrical coordinate system?
Any help should be appreciated.
 

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