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Dy-Dx Questions
Dy-Dx Questions
Use the limit definition of a derivative to find dy/dx.
Find y as a function of a if y" - 4y" - y' + 4y = 0
(1 point) Find y as a function of x if y′′′+64y′=0, y(0)=−1, y′(0)=−16, y′′(0)=−192. y(x)=
Solve the initial-value problem d2ydt2+10dydt+25y=0,y(1)=0,y′(1)=1. Answer: y(t)=
(1 point) Find y as a function of t if 4y′′+28y′+49y=0, y(0)=6,y′(0)=7. y=
The general solution to the second-order differential equation d2ydt2−4dydt+7y=0 is in the form y(x)=eαx(c1cosβx+c2sinβx). Find the values of α and β, where β>0. Answer: α= and β=
Find the general solution to the homogeneous differential equation d2ydt2−23dydt+130y=0 The solution can be written in the form y=C1er1t+C2er2t with r1
A tank contains 1000L of brine with 40kg of dissolved salt. Pure water enters the tank at a rate of 10L/min.
A thermometer is taken from a room where the temperature is 23oC to the outdoors, where the temperature is −6oC. After one minute the thermometer reads 15oC. (a) What will the reading on the thermometer be after 2 more minutes? , (b) When will
(1 point) Assume the world population will continue to grow exponentially with a growth constant k=0.0132 (corresponding to a doubling time of about 52 years), it takes 12 acre of land to supply food for one person, and there are 13,500,000 square miles o
(1 point) A culture of yeast grows at a rate proportional to its size. If the initial population is 8000 cells and it doubles after 3 hours, answer the following questions. 1. Write an expression for the number of yeast cells after t hours. Answer: P(t)=
An unknown radioactive element decays into non-radioactive substances. In 760 days the radioactivity of a sample decreases by 77 percent. (a) What is the half-life of the element? half-life: (days) (b) How long will it take for a sample of 1
(1 point) A bacteria culture starts with 240 bacteria and grows at a rate proportional to its size. After 5 hours there will be 1200 bacteria. (a) Express the population after t hours as a function of t. population: (function of t) (b) What will be th
When a hot object is placed in a water bath whose temperature is 25∘C, it cools from 100∘C to 50∘C in 190s. In another bath, the same cooling occurs in 170s. Find the temperature of the second bath. The temperature of the second bath =
Solve The Given Initial-Value Problem. The DE Is Homogeneous. (X + Yey/X) Dx ? Xey/X Dy = 0, Y(1) = 0
Solve the initial value problem 2yy' + 2 = y2 + 2x with y(0) = 4. To solve this, we should use the substitution u = With this substitution, y = y' = Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). After the substitution from t
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