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}...
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...
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} =...
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...
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 =...