Differential Equations Answers

y(2x-y+1)dx + x(3x-4y+3)dy=0

a.) 2y′′′−7y′′+12y′+8y=0

b.) y"-2y'+5y=e^xsinx

c.) y′' + y = 2xsinx

1. Given an RC series circuit that has an emf source of 100 volts, a resistance of 30 kilo ohms, a capacitance of 5 microfarad and the initial charge of the capacitor is 1 coulomb. What is the current in the circuit at the end of 0.03 seconds? Ans. -5.455 A
2. Consider that an object weighing 50 lb is dropped from a height of 1000 ft with zero initial velocity. Assume that the air resistance is proportional to the velocity of the body. If the limiting velocity is known to be 200 ft/sec, find the time it would take for the object to reach the ground? Ans. 9.985 sec.

1. An RL circuit has emf of 24t volts, a resistance of 10 k-ohms, an inductance of 5H with an initial current of 1 mA. What is the current after 0.05 seconds? Ans. 118.8µA
2. Initially a tank holds 75 gal of a brine containing 12 lb of salt. At t=0, fresh water is poured into the tank at the rate of 3 gal/min, while the well stirred mixture leaves the tank at the rate of 2 gal/min. what is the amount of salt in the tank after 1 hour? Ans. 3.70 lb

1. Find the equation of the curve at every point that passes through the point (0,-1) and which the normal line at any point (x,y) has a slope of – 1/2(x+1). Ans. y=x²+2x-1
2. Given the family of curves x²+y²=cx, find the family of curves of the orthogonal trajectories. Ans. x²+y²=ky

The number of bacteria in a yeast culture grows at a rate which is proportional to the number present. If

the population of a colony of yeast bacteria triples in one hour, find the number of bacteria which will be

present at the end of five hours.

 Using Coefficient Linear in Two Variables, determine the general solution of (𝒙 − 𝟑𝒚 − 𝟑)𝒅𝒙 + 𝟑(𝒙 + 𝟑𝒚 − 𝟑)𝒅𝒚 = 0

A body of unknown temperature is placed in a refrigerator at a constant temperature of 0∘F, If after 20 minutes the temperature of the body is 40∘F, and after 40 minutes the temperature of the body is 20∘F, find the initial temperature of the body.

exponential growth and decay formula and graph