Help with Method of Characteristics - PDE's

  • Thread starter Thread starter rexasaurus
  • Start date Start date
  • Tags Tags
    Method
Click For Summary
The discussion focuses on using the method of characteristics to solve the partial differential equation xux + yuy = 1 with the initial condition u(x,y) = 1 when x² + y² = 1. The user has transposed the equation into the s-t domain and derived expressions for u, x, and y in terms of integration constants. They successfully integrated to find u = s + K1, x = K2e^s, and y = K3e^s. However, they express uncertainty about how to apply the initial conditions to determine the constants. Clarification on incorporating the initial conditions into the solution process is needed.
rexasaurus
Messages
12
Reaction score
0
1. Use the method of characteristics to solve: xux+yuy=1



2. given condition of u(x,y)=1 when x2+y2=1



3. I know I need to transpose into the s-t domain. Using: du/ds=uxdx/ds+uydy/ds=aux+buy
so a=x & b=y...

please help
 
Physics news on Phys.org
I was able to solve for the following:
du/ds=1 integrate to get u=s+K1
dx/ds=x integrate to get x=K2es
dy/ds=y integrate to get y=K3es

I am unsure how to use the IC's
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Solve the given first order Partial differential equation.
  • · Replies 1 ·
Replies
1
Views
1K
How should I find ## x_{2}(t) ## for this nonlinear integro-differential equation?
  • · Replies 6 ·
Replies
6
Views
2K
Solving a Partial Differential Equation with the Characteristic Method
  • · Replies 5 ·
Replies
5
Views
2K
Use Stokes' theorem on intersection of two surfaces
  • · Replies 3 ·
Replies
3
Views
2K
Method of Characteristics, PDE, Jacobian condition Q
  • · Replies 5 ·
Replies
5
Views
2K
Calculate this Integral around the Circular Path using Green's Theorem
  • · Replies 3 ·
Replies
3
Views
2K
Unable to simplify dS (Stokes' theorem)
  • · Replies 1 ·
Replies
1
Views
1K
Solve PDE Method of Characteristics help
  • · Replies 1 ·
Replies
1
Views
5K
PDE and the separation of variables
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Characteristic curves for ##u_t + (1-2u)u_x = -1/4, u(x,0) = f(x)##
  • · Replies 2 ·
Replies
2
Views
3K