The number of arbitrary constants in the particular solution of a differential equationof third order are:(A) 3 (B) 2 (C) 1 (D) 0
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If y=(x+1+x2−−−−−√)n, then (1+x2)d2ydx2+xdydx is
The solution of the equation dydx=1−y21−x2−−−−−−√ is
Which of the following does not represent the orthogonal trajectory of the system of curves (dydx)2=ax
A curve y=f(x) passes through (1,1) and tangent at P(x,y) cuts the x-axis and y-axis at A and B , respectively, such that BP:AP=3, then (a) equation of curve is xyprime−3y=0 (b) normal at (1,1) is x+3y=4 (c) curve passes through 2,8 (d) equation of curve is xyprime+3y=0
The solution of the differential equation dydx+yxlogy=yx2(logy2) 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