Sunday, November 16, 2008

Solving Equations Reducible to Homogeneous Forms

If an equation of the form

dy/dx = [a1x+b1y+c1]/[a2x+b2y+c2] is given

Put x = X+h and y = Y+k

where h and k constants.

h and k are to be determined.

Their values are

h/(b1c2-b2c1) = k/(c1a2-c2a1) = 1/(a1b2-a2b1)

This substitution will give the transformed equations

dY/dX = (a1X + b1Y)/(a2X + b2Y)

The above equation is a homogeneous differential equation.

Solve it and substitute X = x-h and Y = y-k

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