Sunday, November 16, 2008

Solution of Differential Equations Reducible to Linear Form

When the given diff. equation is of the type

dy/dx + Py = Qyn and P and Q are constants or functions of x alone and value of x is not either zero or one, the equation can be reduced to the linear form.


Divide both sides by yn

y-ndy/dx + Py-n+1 = Q

Substitute y-n+1 = v

we get the transformed equation which is a linear equation

dv/dx + (1-n)Pv = (1-n)Q

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