Differential Equations Answers

A thermometer is removed from a room where the

temperature is 70° F and is taken outside, where the air

temperature is 10° F. After one-half minute the thermometer reads 50° F. What is the reading of the thermometer at t  1 min? How long will it take for the

thermometer to reach 15° F?

A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 10° F. After one-half minute the thermometer reads 50° F. What is the reading of the thermometer at t  1 min? How long will it take for the thermometer to reach 15° F?

2 As the biologist for a certain crocodile farm, you know that its carrying capacity is 20,000 crocodiles. You initially release 5000 crocodiles into the farm. After 6 weeks, the crocodile population has increased to 7500. In how many weeks will the population reach 10,000? In how many weeks will the population reach 20,000^ prime

1. Find the general solution of the differential equation using the method

of variation of parameters y′′ + 4y = 4sec(2x)

Calculate the Laplace transform of

• (t) integral from (0 to t) (T)e^(T)dT

Find the general solution for the differential equation

-y"=6x + xe^x

(a) using method of undetermined coefficients

(b) using variation of parameters

(𝑥𝑦²+ 𝑦 − 𝑥)𝑑𝑥 + 𝑥(𝑥𝑦 + 1)𝑑𝑦 = 0

 An RCL circuit connected in series has R = 10 ohms, C = 10^2 farad, L = 1.5 henry, and an applied voltage E = 12 volts. Assuming no initial current and no initial charge at t = 0 when the voltage is first applied, find the subsequent current in the system.

Solve the equation (𝑥 + 𝑠𝑖𝑛𝑦)𝑑𝑥 + (𝑦2 + 𝑥𝑐𝑜𝑠𝑦)𝑑𝑦 = 0

Find the orthogonal trajectories of the following curves (where a is a parameter). r = a(1 + sin θ)