I have a heterogeneous modified Bessel equation: $$z'' +\frac{1}{r}z'-v^2z=G(r),$$
I find the homogeneous solution of it: $$y_h=u_1 I_0 (νr)+u_2 K_0 (νr)$$
and a particular solution via Variation of Parameters: $$y_p=∫[G(r) K_0 (νr)rdr] I_0 (νr)-∫[G(r) I_0 (νr)rdr]K_0 (νr)$$ but with my Boundary condition: $$y(r→∞)=0 $$ $$ y^{'}(r=0)=0 $$ $$ y^{''} (r→∞)=0$$ i get for both constant in homogeneous solution zero. Another quastions what i use for integral boundaries in particular solution $$K_0(0)→∞$$