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

Find the differential equations corresponding to v=(A)/(r )+B .

If p=9, v=3 , then find p is terms of v from the equation (dp)/(dv)=v+1/v^2

The function u=e^x sin x ; v=e^x cos x satisfy the equation a. v(d u)/(dx)-u(d v)/(dx)=u^2+v^2 b. (d^2u)/(dx^2)=2v c. (d^2v)/(dx^2)=-2u d. (d u)/(dx)+(d v)/(dx)=2v

A soap bubble of radius r and surface tension T is given a potential V. Show that the new radius R of the bubble is related with the initial radius by the equation P(R^(3) -r^(3)) +4T (R^(2)-r^(2)) = (in_(0)V^(2)R)/(2) where P is the atmospheric pressure.

Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system of equations u + 2y +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4 then show that the roots of the equation (1/u+1/v+/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+u+v+w=0 and 20x^2+10(a-d)^2 x-9=0 are reciprocals of each other.

Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system of equations u + 2y +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4 then show that the roots of the equation (1/u+1/v+/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+u+v+w=0 and 20x^2+10(a-d)^2 x-9=0 are reciprocals of each other.

Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system of equations u + 2y +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4 then show that the roots of the equation (1/u+1/v+/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+u+v+w=0 and 20x^2+10(a-d)^2 x-9=0 are reciprocals of each other.

If r is the radius, S the surface area and V the volume of a spherical bubble, prove that (i) (dV)/(dt)=4pir^(2)(dr)/(dt)

The Speed Of a particle moving in a plane is equal to the magnitude of its instantaneous velocity, v=|vl= sqrt(v_x^2+v_y^2). (a) Show that the rate of change of the speed is (dv)/(dt)=(v_xa_x+v_ya_y)/(sqrt(v_x^2+v_y^2)) . (b) Show that the rate of change of speed can be expressed as (dv)/(dt) is equal to a_t the component of a that is parallelto v.

Let f: R->R satisfying |f(x)|lt=x^2,AAx in R be differentiable at x=0. Then find f^(prime)(0)dot