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Boundary Value Problem with 5 differential equation and 2 unknown value

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Boundary Value Problem with 5 differential equation and 2 unknown value

I have 3 equation which are one first order equation and two are second order equation

So I decrease one order to match up to first order equation

So I have 5 equation and 2 unknown value which are F` and G`

All of H G F are terms of jeta

Here is attachment that i have to solve

F` and G` are the unknown value

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