Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.y2=a(b2−x2)
A cyclist moving on a level road at 4 m/s stops pedalling and lets the wheels come to rest. The retardation of the cycle has two components: a constant 0.08 m/s2 due to friction in the working parts and a resistance of 0.02v2/m , where v is speed in meters per second. What distance is traversed by the cycle before it comes to rest? (consider 1n 5=1.61).
Statement 1 : The order of the differential equation whose general solution is y==c1cos2x+c2sin2x+c3cos2x+c4e2x+c5e2x+c6 is 3. Statement 2 : Total number of arbitrary parameters in the given general solution in the statement (1) is 3.
From the differential equation of family of lines situated at a constant distance p from the origin.
Let f(x),x≥0, be a non-negative continuous function, and let F(x)=∫0xf(t)dt,x≥0, if for some c>0,f(x)≤cF(x) for all x≥0, then show that f(x)=0 for all x≥0.