So I have a question asking me to solve the PDE Δu = $u_{tt}$ in $R^3$ subject to the initial conditions u(0,x,y,z) = $\sqrt{(x^2 + y^2 + z^2)}$ and $u_t(0,x,y,z) = x^2 + y^2 + z^2$. There is a hint to use the substitution w = ru, but I'm just not sure how to start solving this.
My thoughts are to first convert the PDE to spherical coordinates and then do the substitution, but I'm not sure what it means by find the "radial" solutions. Can someone help me figure out the solution steps?