Find the general solution of the differential equations:xlogxdydx+y=x2logx
A curve C passes through (2,0) and the slope at (x,y) as x+1(x+1)2+(y−3)˙ Find the equation of the curve. Find the area bounded by curve and x-axis in the fourth quadrant.
A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant k is positive). Suppose that r(t) is the radius of the liquid cone at time t. The time after which the cone is empty is
A normal is drawn at a point P(x,y) of a curve. It meets the x-axis at Q˙ If PQ has constant length k, then show that the differential equation describing such curves is ydxdy=±k2−y2 . Find the equation of such a curve passing through (0,k)˙
The general solution of the differential equation, yprime+yϕprime(x)−ϕ(x)ϕprime(x)=0 , where ϕ(x) is a known function, is