# Search results for query: *

• Users: pk415
• Order by date
1. ### Solving U_{tt}=9U_{xx} with Laplace Transforms

We are supposed to work this using Laplace transforms U_{tt}=9U_{xx}; -infty<x<infty U(x,0)=sinx U_t(x,0)=0 The attempt at a solution Let L[U]=\hat{U} L[U_{tt}]=s^2\hat{U}-s(sinx) L[9U_{xx}]=9\hat{U}_{xx} s^2\hat{U}-s(sinx)=9\hat{U}_{xx}...
2. ### First order pde cauchy problem by method of characteristics

Ok, so I can get through most of this but I can't seem to get the last part... Here is the problem xU_x + (y^2+1)U_y = U-1; U(x,x) = e^x Characteristic equations are: \frac{dx}{x} = \frac{dy}{y^2+1} = \frac{dU}{U-1} Solving the first and third gives: \frac{U-1}{x} = c_1 The...
3. ### First Order PDE Cauchy problem Using Method of Characteristics

Homework Statement Ok, so I can get through most of this but I can't seem to get the last part... Here is the problem xU_x + (y^2+1)U_y = U-1; U(x,x) = e^x Homework Equations The Attempt at a Solution Characteristic equations are: \frac{dx}{x} = \frac{dy}{y^2+1} =...
4. ### 2nd order partial differential equation

Thanks Mute So then my integrating factor should be e^{-xy} right? Then I have V = e^{xy}[\int e^{-xy}e^x + f(y)] V = e^{xy}[e^{1-y} \int e^x + f(y)] V = e^{xy}[e^{1-y}e^x + f(y)] V = e^{xy+x-y+1} + e^{xy}f(y) U_y = e^{(x-1)y+x+1} + e^{xy}f(y) And I was thinking I...
5. ### 2nd order partial differential equation

Hello all, this is my first post and I'm having trouble with some homework. Here is the problem: Solve: U_x_y - yU_y = e^x I tried subbing V = U_y then I have V_x - yV = e^x I solve this as a linear equation with an integrating factor of e^{-\frac{1}{2}y^2} and get V =...