The PDE
2∂x2∂2z+2∂y2∂2z+4∂x∂y∂2z=2x2∂x2∂2z+2∂y2∂2z+4∂x∂y∂2z=2x
second order pde can be written in the form:
azxx+2bzxy+czyy+dzx+ezy+fz=g(x,y)
for 2∂x2∂2z+2∂y2∂2z+4∂x∂y∂2z=2x :
b2−ac=4−4=0
this is parabolic equation
for 2x2∂x2∂2z+2∂y2∂2z+4∂x∂y∂2z=2x :
b2−ac=4−4x2
then:
for x=0 :
this is parabolic equation
for x<−2 and x>2 :
b2−ac<0
this is elliptic equation
for −2<x<2 :
b2−ac>0
this is hyperbolic equation
Comments