Non Linear PDE Mathematical Symbols
Not what you're looking for?
I cannot use mathematical symbols. Thus, I will let * denote a partial derivative. For example, u*x means the partial derivative of u with respect to x. Moreover, I will further simplify things by letting p=u*x and q=u*y. Also, ^ denotes a power (for example, x^2 means x squared) and / denotes division. This is the problem:
The PDE is: xp+yq+p+q-pq=u
I need to find a complete integral. I should use Charpit's method, where I find p=P(x,y,u,a) and q=Q(x,y,u,a). I then solve du=P(x,y,u,a)dx+Q(x,y,u,a)dy to obtain f(x,y,u,a)=b, thus giving me u=u(x,y,a,b), a complete integral. Now I have already found the characteristic system to be:
dx/x+1-q = dy/y+1-p = du/u-pq = dp/0 = dq/0. (Is this right?) Please help me solve this system and find the appropriate P and Q for the Pfaffian equation du = Pdx+Qdy. Can you also help me solve this! Please help!!!
Purchase this Solution
Solution Summary
The non linear PDE mathematical symbols are determined.
Solution Preview
Please see the attached solution
Partial differentiation.
The PDE is: xp+yq+p+q-pq=u
I need to find a complete integral. I should use Charpit's method,
Where I find p=P(x,y,u,a) and q=Q(x,y,u,a). I then solve ...
Purchase this Solution
Free BrainMass Quizzes
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.