- #1
coverband
- 171
- 1
Do these equations have two general solutions!?
e.g. z_x + z_y -z = 0
Using the method of characteristics
a=1
b=1
c=-1
d=0
Therefore dx/1=dy/1=dz/z
Taking first two terms: x = y + A
*Taking last two terms: z = Be^y
So general solution is z = f(x-y)e^y
BUT if we took first and last terms: z=Be^x
z=f(x-y)e^x...
e.g. z_x + z_y -z = 0
Using the method of characteristics
a=1
b=1
c=-1
d=0
Therefore dx/1=dy/1=dz/z
Taking first two terms: x = y + A
*Taking last two terms: z = Be^y
So general solution is z = f(x-y)e^y
BUT if we took first and last terms: z=Be^x
z=f(x-y)e^x...