Characteristic Lines for 2D Equations with a Boundary Condition

[andrey21]

Find the characteristic lines for the equation:

2 du/dx + 8x du/dt = 16x




Here's my attempt

a = 2 b = 8x c = 16x

Using dt/dx = b/a = 8x/2 = 4x

t = 2x² + C

C = t₁ -2x₁²

Hence the characteristic is:

t = 2x² + t₁ - 2x₁²

 

[andrey21]

Please any reply would be great, am I correct with my answer??

 

[HallsofIvy]

1. You can't expect people to anwer within two hours. People don't just sit around waiting for a new post!

2. You can get yourself an infraction and even banned for "bumping" threads just to get them moved to the top of the list again.

3. I don't even understand your answer. The characteristic is a relation between x and y. There is no "y" in your answer but there is a "t" which shouldn't be there.

 

[andrey21]

All of the examples I have been given they do not contain a "y", I should have stated the boundary condition is u(x,0) = x^(2).