Math Problem Solver

u(r)=\frac{PK}{\nu}\left[1-\frac{J_0(i r/\sqrt{K})}{J_0(i a/\sqrt{K})}\right]

\langle u \rangle= \frac{PK}{\nu}\left[ 1- \frac{2\sqrt{K}}{ai} \frac{J_1(ia/\sqrt{K})}{J_0(ia/\sqrt{K})}\right]

M(r)=\frac{PK}{D(x)\nu}\left[ \frac{r^2 \sqrt{K}}{2ai} \frac{J_1(ia/\sqrt{K})}{J_0(ia/\sqrt{K})}-K \frac{J_0(ir/\sqrt{K})}{J_0(ia/\sqrt{K})}\right]

D_s'= \frac{P^2K^3}{D(x)\nu^2}\left[ 1+ \left(\frac{2\sqrt{K}}{ai} \right)\frac{J_1(ia/\sqrt{K})}{J_0(ia/\sqrt{K})} +\left( \frac{3a^2+16K}{2a^2}\right)\frac{J_1^2(ia/\sqrt{K})}{J_0^2(ia/\sqrt{K})} \right]-D(x)

using the above equation to D(x) \frac{1}{r}\frac{d }{d r}\left (r\frac{d Q}{d r}\right)=-M \langle u \rangle+ M u - D_s'-D(x), to find Q(r)