# Reducing a Differential Equation of a Special Form to a Homogeneous Equation

Reducing a Differential Equation of a Special Form to a Homogeneous Equation

This Demonstration shows the reduction of a differential equation of the form to a homogeneous differential equation of the form . This case occurs if the system of linear equations , has a unique solution , ; then new variables are introduced by the equations , . If the system of linear equations has no solution or has infinitely many solutions, the differential equation reduces to an equation with separable variables.

y'=F((ax+by+c)/(dx+ey+f))

Y'=F((aX+bY)/(dX+eY))

ax+by+c=0

dx+ey+f=0

x

1

y

1

X=x-

x

1

Y=y-

y

1