The differential equation of the family of circles with fixed radius 5 units and centre on the line y=2is
Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1)=1. If the y−∈tercept of the tangent at any point P(x,y) on the curve y=f(x) is equal to the cube of the abscissa of P, then the value of f(−3) is equal to________
Tangent is drawn at the point (xi,yi) on the curve y=f(x), which intersects the x-axis at (xi+1,0) . Now, again a tangent is drawn at (xi+1,yi+1) on the curve which intersect the x-axis at (xi+2,0) and the process is repeated n times, i.e. i=1,2,3,˙n˙ If x1,x2,x3,,¨xn from an arithmetic progression with common difference equal to (log)2e and curve passes through (0,2)˙ Now if curve passes through the point (−2,k), then the value of k is____
Statement 1 : Order of a differential equation represents the number of arbitrary constants in the general solution. Statement 2 : Degree of a differential equation represents the number of family of curves.
A normal at any point (x,y) to the curve y=f(x) cuts a triangle of unit area with the axis, the differential equation of the curve is
A normal is drawn at a point P(x,y) of a curve. It meets the x-axis and the y-axis in point A AND B, respectively, such that OA1+OB1 =1, where O is the origin. Find the equation of such a curve passing through (5,4)