[qquad [v,=(A)/(r)+B,(" where "A,B" constants ")],[(p*T)/(dx),(d^(2)gamma/2)/(dr^(2))+(2)/(r)(dv)/(dr)=0]]

Show that,v=(A)/(r)+B satisfies the differential equation (d^(2)v)/(dr^(2))+(2)/(r)*(dv)/(dr)=0

Show that , v = (A)/(r) + B satisfies the differential equation (d^(2) v)/(dr^(2)) + (2)/(r) .(dv)/(dr) = 0

(dv)/(r^(2))=4pidr, when r=0, v=0

Show that, v = A/r + B satisfies the differential equation (d^2v)/(dr^2)+2/r.(dv)/(dr)=0

pv^a=c (a and c are constants) then show that v^2(d^2p)/(dv^2)=a(a+1)p .

If x=sint ,y=sinp t ,"p r o v et h a t" (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y=0.

Evaluate, int_(r1)^(r_2) (kq1q2)/r^2 dr.

If r=2(1-costheta) , then show that, int_(0)^(pi)sqrt(r^(2)+((dr)/(d theta))^(2))d theta=8