D'Alembert's solution for the one-dimensional wave equation for a semi-infinite string.

Find the solution to: PDE: u*xx-c(to the power of negative k)u*tt=0 , 0=0 BC: u*x(0,t)=0 , t>=0 This BC corresponds to a string with its end point free to move in a vertical direction. I will use * to symbolize a partial derivative. For example, u ...continues

PDE : Complete solution to a non-linear equation.

The PDE is: xp + yq + p + q -pq = u which gives: p(x+1) + q(y+1) - pq - u = 0 Now, I need to find a complete solution. I have set up my characteristic system to be: dx /x+1-q = dy /y+1-p = du /u-pq = dp /p(pq-u-1) = dq /q(pq-u-1) Help! I cannot solve any of these integrals. I need p = P(x,y,u,a) and ...continues

PDE : Riemann's Method for Solving Cauchy Problem

Hello. Thanks for help! I will use * to indicate a partial derivative. For example, u*x denotes the partial derivative of u with respect to x. This is the probelm: Use Riemann's method to solve the Cauchy problem: u*xx + 4u*xy +3u*yy = 1, u=1 and u*n = square root of 5 times x, on the intial curve y=2x. If this ...continues

D'Alembert's solution for the one-dimensional wave equation for a semi-infinite string

Find the solution to: PDE: u*xx-c(to the power of negative k)u*tt=0 , 0 ICs: u(x,0)=f(x) and u*t(x,0)=g(x), x>=0 BC: u*x(0,t)=0 , t>=0 This BC corresponds to a string with its end point free to move in a vertical direction. (Please remember to include to boundary condition in your solution. Thanks very much!) ...continues

Green's function

Hello. Thank you for taking the time for helping me. The following is the problem which I need to solve (there are actually two parts): I need to construct Green's function for the Dirichlet problem (Laplace's equation) in the upper half plane R={(x,y) : y>0} and I must derive Poisson's integral formula for the half plane. ...continues

solving a Pfaffian equation for a complete integral

Hello. Thank you for taking the time to help me. I cannot use mathematical symbols, thus, * will denote a partial derivative. For example, u*x denotes the partial derivative of u with respect to x. To simplify things, I will let p=u*x and q=u*y. Furthermore, I will use ^ to denote a power. For example, x^2 means x squared. Also, ...continues

Non linear PDE.

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: T ...continues

Cauchy problem

I cannot use mathematical symbols. Thus, I will let * denote a partial derivative. For example, u*x means the partial derivative of us with respect to x. Furthermore, I will let u*x=p and u*y=q. Also, I will let ^ denote a power. For example, x^2 means x squared, and, I will let / denote division. Here is my problem: The PDE ...continues

Partial Differential Equation simplification

I am trying to simplify Y(y) using the boundary condition Y(1) = 0. Please find details on the attached file. Thanks

Dirichelet problem

I need to use separation of variables to solve Laplace's equation in the annular sector: 1< r<2, 0< theta< pi/2, u(1,theta)= f(theta), u(2,theta)=0, u(r,0)=0, u(r,pi/2)=0 Thank you!