Differential Equations Answers

An inductance of 1 henry and a resistance of 1 ohm are connected in series with a constant EMF of E volts. If the current is initially zero, and is equal to 10 A after 5 seconds, find E.

Brine containing 3 lbs./gal of salt enters a large tank at the rate of 2 gals / min and the mixture well stirred leaves at 1.5gal / min. If the tank contains initially 100 gal of water, with 4 lbs. of dissolved salt.

a ) Find the amount of salt in the tank at any time t in minutes .

b ) Find the amount of salt in the tank after 4 minutes.

Use the Bisection method with 3 iterations to find solutions for f(x) = x3 + x - 4 on interval [1; 4].

The fourth-degree polynomial

f(x) = 230x4 + 18x3 + 9x2 - 221x - 9

has two real zeros, one in [-1; 0] and the other in [0; 1]. Attempt to approximate these zeros to within

10-2 using the

(a)

Secant method(Use the endpoints of each interval as the initial approximations),

(b)

Newtons method(Use the midpoints of each interval as the initial approximation)

Under a certain condition , cane sugar in water is converted into dextrose at a rate proportional to the amount that is unconverted at any time . If 75 kg at t =; 0, 8 kg are converted during the first 30 minutes , find the amount converted in 2 hours .

Find the solution:

2(dS)/(dt) - S/t = 5t^3 S^3