Show that the differential equation (x−y)dxdy=x+2yis homogeneous and solve it.
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.y2=a(b2−x2)
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.y=ae3x+be−2x
Prove that x2−y2=c(x2+y2)2is the general solution of differential equation (x3−2xy2)dx=(y3−3x2y)dy, where c is a parameter.
Find the particular solution of the differential equation (1+e2x)dy+(1+y2)exdx=0, given that y=1whenx=0.
Find the order and degree, if defined, of each of the following differential equations:(i) dxdy−cosx=0 (ii) xydx2d2y+x(dxdy)2−ydxdy=0 (iii) yprimeprimeprime+y2+eyprime=0
In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?