Find the equation of the family of all erhogonal trajectories of the family ofcircles which pass through origin and hav centres on the y-axis.
State Newton s law of cooling. If the temperature of the air is 30^{0}C and thetemperature of the body drops from 80°C to 60^{0}C in 10 minutes. What will beits temperature after 20 minutes.
Solve (x^{2}D^{2}+4xD+2)y=(logx/x)^{2},x>0 , where D=d/dx
Solve d^{2}y/dx^{2}-6dy/dx+13y=20e^{3x}cos(2x+5)
Solve the initial value problem y^{2}y -y^{3}tanx=sinxcos^{2}x,y(0)=1
the tunction f(z)= (z)^{2}/z,z≠0 0,z=0 suntistes -Rieman equations at z=0 Does f (0) exist?`
Evaluate ∫0^{π/2α}αsinαxdx,α>0 by using Leibniz formula.`
find the length of the curve y=ln(e^{x}+1/e^{x}-1) from x=1 to x=2 `
A 3 cm diameter tube is used to measure the binary diffusion coefficient of water vapor in air at
20°C at an elevation of 1600 m where the atmospheric pressure is 83.5 kPa. The tube is partially
filled with water, and the distance from the water surface to the open end of the tube is 40 cm.
Dry air is blown over the open end of the tube so that water vapor rising to the top is removed
immediately and the concentration of vapor at the top of the tube is zero. In 15 days of
continuous operation at constant pressure and temperature, the amount of water that has
evaporated is measured to be 1.23 g. Determine the diffusion coefficient of water vapor in air at
20°C and 83.5 kPa. Given, the pressure of water at 20°C is 2.34 kPa.