Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.ax+by=1
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The gradient of the curve passing through (4, 0) is given by if the point (5, a) lies on the curve, then the value of a is
The degree of differential equation satisfying the relation1+x2−−−−−√+1+y2−−−−−√=λ(x1+y2−−−−−√−y1+x2−−−−−√) is
The particular solution of the differential equation sin−1(d2ydx2−1)=x, wherey=dydx=0 whenx=0, is
Find the time required for a cylindrical tank of radius 2.5 m and height 3 m to empty through a round hole of 2.5 cm with a velocity 2.5h
being the depth of the water in the tank.
The solution of differential equation dxy(2x4+y)dy=(1−4xy2)x2 is given by
The solution of the differential equation dx(x+2y3)dy=y is
Suppose that a mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the diameter of the ball decreases from 2cm to 1cm in 3 months, how long will it take until the ball has practically gone?
What is the degree of the differential equationkd2ydx2=[1+(dydx)3]3/2, where k is a constant?