The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y=c1+c2cosx+c3sinx,(−[infinity],[in finity]) y=c 1 +c 2 cosx+c 3 sinx,(−[infinity],[infinity])
y'''+y′=0,y(π)=0,y′(π)=2,y''(π)=−1 y +y =0,y(π)=0,y ′ (π)=2,y ′′ (π)=−1

Water at the rate of 1 kg/s is forced through a tube with a 2.5 cm inner diameter. the inlet water temperature is 15°c, and the outlet water temperature is 50°c. the tube wall temperature is 14°c higher than the local water temperature all along the length of the tube. what is the length of the tube?

The characteristic roots of a dynamic system are: 1.7920 1.8160 i, -1.7920 1.8160 i, -0.4160 what is the order of this system? what are the settling time and damping ratio of the system?

An electric kettle is made out of stainless steel, weighs two pounds (when empty) and is equipped with a heating element that consumes 2 kw of electricity. assuming that the water and the kettle are at the same uniform temperature at any moment of time, calculate the shortest possible time to bring 2 quarts of water from room temperature to the onset of boiling