Question

Please help in Partial Differential Equations...

Answer 1

@ganeshie8

Answer 2

@texaschic101 please help

Answer 3

@Zarkon please help

Answer 4

@Michele_Laino

Answer 5

The first part I got the solution..

Answer 6

first part:
I got this:
\[\frac{{dz}}{{dt}}\left( {\frac{2}{\alpha } + \frac{3}{\beta }} \right) = 1\]

Answer 7

I'm sorry, I'm not good with albraic theory of PDEs, I'm good with symmetry properties of PDEs

Answer 8

I used the method known as Cauchy problem, solved by the method of characteristics.. we ll I just wanted to know, see the second part of the question, what happens when ... I dont have any idea what to do..

Answer 9

yes I know that there is the method of characteristics, nevertheless I never studied it

Answer 10

Its ok.. But still if you know someone who may help, let me know..

Answer 11

if \(3 \alpha- 2 \beta=0\) we have a singularity for \(z(x,y)\), maybe we have to request that the sum between the second term and the third term inside the parentheses of your expression is equal to a constant value

Answer 12

I think that @ganeshie8 can help you!

Answer 13

YEs I noticed that the denominator is 0 in the given condition.
Well my book says that this type of problem is known is Cauchy problem and dont have any unique solution(when I read the theory).. But it is not showing any method to solve.. So

Answer 14

I am confused

Answer 15

I understand, nevertheless I'm not able to help you, I'm sorry!

Answer 16

ok anyway thanks you took you time to help me.:)

Answer 17

:)

Answer 18

@freckles

Answer 19

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&uact=8&ved=0CDMQFjADahUKEwiT89vMsNTIAhVLkA0KHZxvApU&url=http%3A%2F%2Fmath.iisc.ernet.in%2F~prasad%2Fprasad%2FLinear_Quasi.pdf&usg=AFQjCNGuItR4GXDvBCim3ELedfgo5qbLCQ&sig2=kfKhiLr-8cIty_5s9nRfhQ
I'm trying to study slides 20-26 here
it looks like this might be helpful