Find the differential equation of all the ellipses whose center is at origin and axis are co-ordinate axis.
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The solutions of (x+y+1) dy=dx are
The solution of the differential equation 3extanydx+(1−ex)sec2ydy=0 is
The solution of dydx=1−x2−y2+x2y2−−−−−−−−−−−−−−−√ is
The population of a country doubles in 40 years. Assuming that the rate of increase is proportional to the number of inhabitants, the number of years in which it would treble itself is
If for the differential equation y′=yx+ϕ(xy), the general solution is y=xlog|Cx|, then ϕ(x/y) is given by
A body at a temperature of 500F
is placed outdoors where the temperature is 1000F
. If the rate of change of the temperature of a body is proportional to the temperature difference between the body and its surrounding medium. If after 5 min the temperature of the body is 600F
, find (a) how long it will take the body to reach a temperature of 75 0
F and (b) the temperature of the body after 20 min.
The solution of the differential equation dx(x+2y3)dy=y is