The rate of decay of radium is proportional to the amount remaining. Prove that the amount remaining at time t is given by where is the amount of radium at t = 0.
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Find the curve whose subtangent is of constant length
Find the curve whose subnormal is constant.
The tangent at any point P of a curve meets the axis of X at T. Find the curve for which OP = PT, O being the origin.
Find the orthogonal trajectory of x2 – y2 = a2
Show that ydx – 2xdy = 0
represents a system of parabolas with common axis and tangent at the vertex.
Show that the solution of the general homogenous equation of the first order and degree, is
where v =
Find the curve which passes through origin and is such that the area included between the curve, the ordinate, and the axis of x is k times the cube of that ordinate.
The normal to a curve meets the axis of x at G. If the distance of G from the origin is twice the abscissa of P, prove that the curve is a rectangular hyperbola.
Find the curve which is such that the portion of the axis of x cut off between the origin and the tangent at any point is proportional to the ordinate of that point.
Find the orthogonal trajectory of the family of curves
