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