Find the equation of the family of curves with slope 2x.

Solve y’ = ySecx.

Find the DE for the family of circles with center on the y – axis.

Radium decomposes at the rate proportional to the amount present. In 100 yrs, 100 mg becomes 96 mg. What is the percentage remaining after 100 years?

Mosquito population increase by 2500 + 8e^t per week with t in weeks. By how much did the mosquito population increased between the fourth and the eighth week?

Find the Orthogonal Trajectory to the family of parabolas y^2 = 2x + C.

Solve the DE dy = xdx if the curve passes through (1,0)

A 400gal tank initially contains 100gal of brine containing 50lb of salt. Brine containing llb of salt per gallon enters the tank at the rate of 5gal/s and well mixed in the tank flows out at the rate of 3gal/s. How much salt will the tank contain when it is full of brine?

According to Newton's law of cooling, the rate at which the substance cools in air is directly proportional to the difference between the temperature of the substance and that of air. If the temperature of the air is 30°C and the substance cools from 100°C to 70°C in 15 minutes, how long will it takes in minutes to cool from 100°C to 50°C?

The population of a certain bacteria grows at the rate which s proportional to the amount present. It doubles in 2 yrs. If in 3 yrs there are 20000 of bacteria present, how many is present initially?

Find the differential equation of the family of lines that passes through the origin.

The differential equation of the family of circles with center at the origin is,

The current I following in an RL circuit is given by I = (E/R) (1 – e^Rt/L), where E is the voltage applied to the circuit, R is the resistance and L is the inductance. Express I in terms of E and R when t = L/R.

Solve the differential equation y” – 4y’ + 3y = sin x.

Which of the following equations is an exact DE?

Given is x(y-1) dx – (x+1) dy = 0 and x = 4 when y = 2, find y when x = 2.

The rate of virus spread is jointly proportional to those infected and uninfected people. If there are 5000 inhabitants at the start of the year and after a week there were 160 people infected, after 2 weeks there are 1200 people infected, how many days will there be for 1500 people to be infected?

An object falls from rest. If the velocity of the object before it reached the ground is represented by the differential equation dv/dt plus v per 10 equals 32, ft/sec^2, find the velocity of the object in ft/sec after one second.

The time rate of change of a rabbit population P is proportional to the square root of P. At time t = 0 (months) the population numbers 100 rabbits and is increasing at the rate of 20 rabbits per month. How many rabbits will there be one year later?

Given an RL circuit with a transient current equation of I = (E/R)(1 – e^Rt/L). Find the current at t = L/R.

Which of the following is an exact DE?

Find the differential equation of the family of lines passing through the origin.

In a room temperature of 25°C, a steel ball at 120°C cools down to 80°C in 20 minutes. Find its temperature after one half hour.

If dy = x^2 dx; what is the equation of y in terms of x if the curve passes through (1, 1)?

Determine the differential equation of the family of lines passing through (h,k).

The solution of the differential equation dy/dt = ky, with initial condition y = 1 when t = 0, is,

A motorboat weighs 32000 lb and its motor provides a thrust of 5000 lb. Assume that the water resistance is 100 pounds for each foot per second of the speed v of the boat. Then 1000 dv / dt = 5000 – 100v. If the boat starts from rest, what is the maximum velocity that it can attain?

A body moving in a straight line has an acceleration equal to 6t^2, where the time (t) is measured in seconds and distance (s) is measured in feet. If the body starts from rest, how far will it move during the first 2 sec?

Suppose that at time t = 0. 10,000 people in the city with population of 100,000 people have heard a certain rumor. After one week, the number of those who have heard it has increased to 20,000. Assuming that is satisfies a logistic equation, when will 80% of the city's population have heard the rumor?

The intensity of light at a depth x meters below the surface of the lake satisfies the differential equation dI/dx = -1.4 I. At what depth is the intensity half the intensity lo at the surface where x = 0?