The differential equation which represents the family of curves y=c1ec2x, where c1andc2are arbitrary constants, is
The differential equations , find the particular solution satisfying the given condition:[xsin2(xy)−y]dx+xdy=0;y=4πwhen x = 1
Show that the family of curves for which the slope of the tangent at any point (x, y) on it is 2xyx2+y2, is given by x2−y2=cx.
Form the differential equation representing the family of curves given by (x−a)2+2y2=a2, where a is an arbitrary constant.
Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:y=1+x2 : yprime=1+x2xy
The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20, 000 in 1999 and 25000 in the year 2004, what will be the population of the village in 2009?