In a bank, principal increases continuously at the rate of 5% per year. An amountof Rs 1000 is deposited with this bank, how much will it worth after 10 years(e0.5=1.648)
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The general solution of the differential equation, yprime+yϕprime(x)−ϕ(x)ϕprime(x)=0 , where ϕ(x) is a known function, is
The force of resistance encountered by water on a motor boat of mass m
going in still water with velocity v
is proportional to the velocity v˙
when its velocity is v0,
then engine shuts off. Find an expression for the position of motor boat at time t
and also the distance travelled by the boat before it comes to rest. Take the proportionality constant as k>0.
The solution of the differential equation dx(x+2y3)dy=y is
The slope of the tangent at (x,y) to a curve passing through (1,4π) is given by xy−cos2(xy), then the equation of the curve is
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
Let f:[1,∞] be a differentiable function such that f(1)=2. If 6∫1xf(t)dt=3xf(x)−x3 for all x≥1, then the value of f(2) is
From the differential equation of family of lines situated at a constant distance p from the origin.
then find y(x)