Recent content by galuoises

Thank you so much!

Pardon me, I write the uncorrect differential equation: the problem is at the second order \frac{d^2}{dx^2}f(x)=a f(x) + b f^3 (x) with the boundary f(0)=0,\ f(+\infty)=f_0

I would like to solve the non linear ODE \frac{d}{dx}f(x)=a f(x)+ b f^3 (x) with the boundary f(0)=0\quad f(+\infty)=f_0 How to find analitical solution?

Nice trick! Thank you so much!

I have the integral \int_{-\infty}^{\infty}dx \int_{-\infty}^{\infty}dy e^{-\xi \vert x-y\vert}e^{-x^2}e^{-y^2} where \xi is a constant. I would like to transform by some change of variables in the form \int_{-\infty}^{\infty}dx F(x) \int_{-\infty}^{\infty}dy G(y) the problem is...

Thank you so much Ben Niehoff! Sorry for the notation for the variable x, HallsofIvy, I intended it is a vector x\equiv(x,y,z) and Δ\equiv\partial_{xx}+\partial_{yy}+\partial_{zz}

Someone know how to uncouple this system of pde? Δu_{1}(x) + a u_{1}(x) + b u_{2}(x) =f(x) Δu_{2}(x) + c u_{1}(x) + d u_{2}(x) =g(x) a,b,c,d are constant. I would like to find a solution in one, two, three dimension, possibily in terms of Green function...someone could help me, please?