Find the particular solution of the differential equation extanydx+(2−ex)sec2ydy=0, given that y=4π when x=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?
The Integrating Factor of the differential equation (1−y2)dydx+yx=ay , (−1<y<1)is
(A) y2−11 (B) y2−11 (C) 1−y21 (D) 1−y21
Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:y=ex+1:yprimeprime−yprime=0
The general solution of the differential equation yydx−xdy=0is(A) xy=C (B) x=Cy2 (C) y=Cx (D) y=Cx2
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 a differential equation representing the given family of curves by eliminating arbitrary constants a and b.ax+by=1
The general solution of the differential equation exdy+(yex+2x)dx=0is(A) xey+x2=C (B) xey+y2=C (C) yex+x2=C (D) yey+x2=C